A Texas cop who died a few years ago had a site where he wrote about gun and ammo tests. He fired Federal, Remington, and Winchester loads like you mean from both snubs and four-inch guns. He provided photos of expanded bullets from the usual test media. The Winchester performed well from four-inch, but expanded just slightly from snubs. It was still better than a full wadcutter bullet looks. The Federal was a little better from snubs, and the softer Remington lead bullet expanded quite well from both barrel lengths. Think expansion in excess of .50 caliber.
Assuming that you get a good hit in tough muscle tissue or on bone, I think you'll get good expansion from a three-inch barrel.
I've done considerable research over several decades on this and consulted engineers in the industry to whom ordinary shooters have no access. (I was a gun writer with a masthead listing at one magazine and valid writing credits at other titles.)
I got feedback never printed, except in my own articles. I was also, I believe, the first to explain in print the reason why hot 125 grain .357 loads were wrecking K-frame .357's.
Lee Jurras at Super Vel told me that my three-inch barreled M-36 should give about 85 FPS added velocity over a true snub. The Federal PR man then had engineers test their 129 grain JHP from both two and three-inch .38 revolvers, NOT pressure barrels. The figures were right around what Jurras said was true for his brand. This Fed. ammo was Hydra-Shok.
Finally, I got a detective whom I know (he is or was a member here) to check shooting results re 145 grain .357 Silvertip loads and the FBI .38 round.
These were actual autopsy results; not gelatin tests.
The cartridge is pretty effective.
The best results I got were from a Dallas officer working a bad part of town. He used his M-64 with four-inch barrel and that FBI load (also Dallas issue) to kill six felons, with no stopping power problems. I think the three-inch barrel will give almost as good results as the four-inch, especially with the softer Remington load, IF the Rem. is loaded to stated velocity.
I use the FBI/Dallas/Chicago/ Dade load in my .38's and use it in .357's that I think may be fired indoors, where Magnum blast and penetration are handicaps.
I also use Speer's Short Barrel load in two and three-inch barrels, but if I needed penetration plus reasonable expansion, that FBI load would be my choice in a lead HP .38 round.
When the RCMP went to 9 mm autos, the reason was to get magazine-fed guns that could be reloaded quicker than a revolver. They stated that they were satisfied with the stopping power of their lead Plus P HP ammo, which was loaded a bit hotter than typical US rounds of that type. I understand that they got about 1,000 FPS from the 158 grain lead loads in their five-inch Model 10's.
Massad Ayoob shot pigs in a slaughterhouse with both .380 autos and the snub .38, with the FBI load. The S&W .38 always penetrated the pigs' skulls and killed them. The .380 bullets sometimes glanced off and just caused suffering.
This information should convince you that you are on solid ground to use that old lead FBI load in a three-inch barrel.
The reason why the FBI went to the 147 grain JHP was that they needed better penetration in auto bodies. I don't know if the lead load was adequate against auto glass. Ask SIG P-220, who retired from the Bureau a year or two ago. PM him, or make an open post here for his attention.