Apparently, 357 Magnum 125-grain JHP ammunition has demonstrated itself to be the handgun ammunition having the best one-shot stop performance.
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1. In 357 Magnum revolvers having [nominal] 2-inch barrels, what results occur with this class of 357 Magnum ammunition in ballistic gel or other standardized test media?

Despite the evidence favoring 357 125-grain as superior defensive ammunition, I am partial to 38 Special +P 158-grain LSWC-HP ammunition. And I am strongly considering Buffalo Bore's 38 Special +P 20A/20 158-grain LSWC-GC-HP ammunition that is a substantial ballistic improvement over the lesser LSWC-HP.

2. In the same 357 Magnum revolvers having [nominal] 2-inch barrels, what results occur with Buffalo Bore's 20A/20 ammunition in ballistic gel or other standardized test media? I am especially interested in how the 125-grain 357 and 38 Special 20A/20 compare when test media are "harder," such as car front windshields and the "layers of denim" barriers.

Again, despite evidence, I am predisposed to believe the 20A/20 will demonstrate as superior. What I believe will never happen in this era of semiautomatic pistols being ubiquitous in police holsters is that 20A/20 ammunition will be used in a sufficient number of justified shootings to verify any test media superiority. That is the reason why I seek information only in testing.

BB 20A box says 1000 fps muzzle velocity and 351 lbs of muzzle energy,
but those are minimums. Google Buffalo Bore 20A tests. Lots of good
statistics. Using their own short barrel revolvers they exceed the 1000 MV
and 351 ME. There are also a couple of youtube tests showing this round
being fired into ballistic gel and the results.
The legendary .357 125-gr. JHP +P, for years number one in stopping
power, produced 1200+ MV and over 400 ME. But they probably used
revolvers with 4" barrels.
I believe the Buffalo Bore 20A .38 Spl. would match or maybe even
exceed the .357 load if both were fired from the same revolver with
2" barrel. If you find out, let us know.

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In Omnia Paratus

I really sort of wish the whole "one-shot stop statistics" thing had never seen the light of day. There is absolutely nothing scientific or statistically valid about the stats. First of all, a "stop" is not really defined, other than the person shot stops what they were doing before they got shot. Second, it is all based on anecdotes, and only anecdotes of reported shootings picked up by the "researcher", which equates to a mighty small percentage of all shootings. No accounting whatsoever of shot placement is made -- a "stop shot" might have been delivered center-of-mass, or might have just taken the bad guy's pinky finger off. During the era when these "stats" were being compiled, the far-and-away most common police load was the .357 125 JHP -- so small wonder it would come out on top.

I am not for one minute saying that .357 125 JHP loads are not effective; intuition combined with common sense would dictate that it should be highly effective. But common sense and experience would also dictate that a huge percentage of people who are shot in a typical self-defense scenario will stop what they are doing at the time that they get shot, regardless of what they get shot with. The same common sense should tell anyone that a good hit with a .357 should outperform a good hit with a .25 ACP, but the operative part of the equation is the "good hit" part. If you can shoot out a gnat's eye with a .22, but can't hit a barn door with a .357 -- go with the .22, regardless of what any "statistics" say.

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Pisgah

One of the events that is pivotal in the history of firepower second-guessing, is the 1986 FBI Miami Shootout.

https://en.wikipedia.org/wiki/1986_FBI_Miami_shootout

Thirty years later, there is still no answer in the realm of handguns, except to use one until you can get to your long gun.

The data isn't all "anecdotal". A local detective checked on shootings here with Winchester's 145 grain Silvertip .357. He told me that it was almost too effective.

His words, and I guess he's squeamish. He wore a 9mm Glock until retirement.

Both 2.5 and four-inch barrels were involved, but I don't know distances and shot placement.

This left me with a lot of respect for that load. It'll often crack 1200 FPS even from a three-inch barrel.

I have first hand reporting from Iraq on how well the military 9mm load fares, from my son. When well placed, it did the job. And the late David W. Arnold was more than a gun editor. Before moving to the USA, he was a senior police official in Rhodesia and had access to combat reports from the terrorist war there. He told me that the 9mm usually worked.

I believe some people's "anecdotes." And I believe that the better .357 loads are as good as it gets for shooting people and some dangerous animals.

And I believe the cop who told me that he shot a fleeing felon four times through the chest with a .44 Magnum and the man ran for over a block before falling. That officer went to a S&W M-19 .357. I don't think the .44 bullets opened up well in a human. But that guy he shot must have been highly adrenalized to go that far after even the first shot.

Near total agreement.

Having typed that, prior to the test protocols/research that followed the 1986 altercation - that focused on semiautomatic ammunition - how did police departments, FBI, and other paramilitary organizations choose their standardized ammunition? The Thompson-LaGarde (spelling??) tests of the early twentieth century are well known, at least in anecdotal form. (They are available for download at no cost.) Having read the test series in its entirety, I gotta report that the 45 ACP ballistic decision was not obvious, not at all obvious.

Inferences drawn from these tests apparently made no impression on decision makers of the myriad paramilitary organizations. They were using 32 Colt/S&W and 38 S&W ammunition, then upgraded - WHY this? - to 38 Special 158-grain LRN. In the 1930s the FBI and [many??] state highway patrols upgraded to 357 Magnum. Why the FBI did it I don't know. Perhaps the panache of having the biggest boomer was the equivalent of trap shooters wearing their "scare jackets" covered with award patches to intimidate competitors. At least the highway patrols made sense. The new boomer would penetrate and disable automobile engines and body metal at longish range while previous revolver ammunition would not.

All of which brings me back to choosing "A" rather than "B" or "M." In muzzleloading every hunting rifle I own is based on the adage: There's no substitute for cubic inches. Not only do I have sensible reasons for my decisions. I have a test procedure for projectiles that makes sense for my specific application. I cannot hogtie a bunch of elk and shoot them, then quickly dissect them.* What I do is decide what results have meaning. Identify a particular projectile at a specific muzzle velocity (and impact velocity) that has a long-term record of excellence. I test it. Its results I refer to as my basis projectile - call it "A." I then replicate the test series with muzzleloading projectiles on a "pass-fail" decision. Not only am I comfortable with the method. It works. Of course, test results, so far, demonstrate the muzzleloader projectiles achieve superior test results. That's okay. It doesn't invalidate my basis projectile. When having but a single shot every 90 seconds, "Too much of a good thing is . . . simply marvelous."
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*Trad Gang.com: Ashby Reports
Ashby Reports
Several years ago, an American optometrist retired to Australia where he hunted and culled buffalo in the Northern Territory. His goal was to identify specific characteristics of broadhead-arrow combinations that achieve best penetration and destruction on these huge animals. He used different broadhead and arrow combinations with traditional bows.

The information within these reports is detailed, cogent, useful, and fascinating. You may find its information valid for game hunting, possibly for defensive shooting. Dr. Ashby's procedures and thoroughness might indicate a method to test handgun bullets via analogy.

Not to be overly contentious, but everything you're saying here pretty much defines the term "anecdotal". I don't doubt a thing your friend has told you, and am sure every event he related actually happened, but absolutely nothing even near scientific can be concluded from any of it. The fact is, I know of a man killed stone dead, instantly, by one shot from a .25 Baby Browning that actually passed through an automobile windshield before hitting him -- but I certainly wouldn't consider that an endorsement of the unqualified effectiveness of the .25 ACP.

Now, of course, there have been numerous attempts to scientifically quantify effectiveness of various handgun loads, with some experiments being better-designed than others, but the fact remains that beyond the intuitive idea that "bigger is better", there has never been any valid conclusion over which is definitively the best. There are simply too may variables to consider.

The only advice I can give about what load NOT to depend on is -- whatever load you would not mind at all being shot with. ;-)

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Pisgah

Trying Buffalo Bore in several calibers, in different guns, I have found erratic results-certainly too erratic to depend on it to protect my life. Elsewhere, I noted the results of shooting my 357 Sig and 10mm Glocks this last weekend. Group sizes (in all calibers) were larger with BB and the only FTF was a BB. I have noted similar results in 9mm, 380 acp, and several others.

Groo here
The "stopping power" thing has more than it's ink used.
I like Keith's "Slap".
That is the physical reaction upon the impact of the bullet.
If there is no reaction on impact , there will be little effect or "stop".

One thing most forget about the Thompson-LaGarde test is the conditions at the time.
The test against steers is most important as most armies still used
horses. [ the way you stop a charge is to shoot the horse , not the rider]
Shooting people was really secondary.[a horseman on foot is called a target]
If you want info on shooting people, reed the English records late 1800 early 1900's.. [Against the Fuzzy-Wuzzy's , Zulu's and such]
The English keep almost as good records as the Germans and had a larger Empire.

I have to agree. I think people expect that a shot to the torso knocks their opponent out much like a punch to the head. The problem is that no scientific evidence can show that a mechanism capable of that exists.

I like to look back in history in order to clear up this issue in my own mind. The .36 Navy caliber Colt was issued during the Civil War and I have yet to find complaints about its effectiveness. The .36 caliber was the basis for a series of .38 caliber cartridges that were loaded to produce power levels similar to the .36 Navy. The .38 Long Colt was the most powerful of the bunch but was said to be impotent. That just doesn't make any sense to me.

One facet of the T-L tests was that 30 Mauser and 9x19 mm were identified as comparable or superior to 45 Colt 255 grain ammunition for several tests, and the 455 Webley round was yet more effective, again, for several tests. These counter-intuitive findings are the reason I mentioned that the War Department's choice of what became the 45 ACP was not an obvious decision.

Regarding the Mauser and Luger ammunition, my guess is that hardball at high velocity [for handgun ammuntion of the era] hitting large bones would crack or break the bone, plus create a bunch of secondary [bone fragment] missiles.

Just a guess.

When I was working as a firefighter it was in a community that was "ranked" as one of the most dangerous in California and the nation. Naturally, we would be there to pick up the pieces. When I first started, the PD carried S&W Model 66 and they were loaded with .357 125 grain JHP. I never saw a criminal that needed to be shot a second time. The effect of one well placed round was good enough.

As things changed the department went to semi-automatics and the officers had the choice of either providing their own or use a department provided S&W in either .45 ACP or .40 S&W. Most opted to buy their own 1911-A1.

Once again, we were there to pick up the pieces. It was the first time I heard the phrase, "they all fall to hardball."

However, when it was approved for them to carry Glock's, I saw the aftermath of .40 S&W shootings. Criminals withstood multiple hits better than they did with either .357 Magnum or .45 ACP. I'm certainly not a ballistics guru or a forensic scientist, but I saw what I saw and I saved those that could be saved.

As an aside, the criminals in that community used whatever they could get their hands on. More often than not, their killings were done in an ambush. On more than one occasion we had firefighter's fall and get injured running on all the spent brass.

The majority of that brass was either 9mm or 7.62x39mm.

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I believe in the wadcutter.