Which version of the 625-8 do you have? I'll bet it's the 625 JM. As for how I knew that, it's pretty simple, the JM features an ECM rifled barrel and the PC version has cut rifling. I tried just 50 rounds of Blaser LRN 38 spl in my model 620, which also features an ECM barrel, and it took 12-14 hours of scrubbing to get the lead out of the barrel. As I found out the ECM barrels are EXTREMELY particular about the lube used with a lead bullet. As a result I only shoot jacketed or plated bullets in my revolvers with ECM barrels. BTW, those revolvers are my 610-3, 620, and 625 JM.
Now for some good news that should ease your mind. That is that Federal Champion 45 ACP ammunition uses plated bullets. I know that for a fact because I broke down a couple of rounds that had primers installed sideways to recycle the casings. It was a bit of a surprise when I found the bullets were not actually FMJ as marketed but are instead plated. Now the good news about this, if you haven't shot any Federal Champion in your 625 I can tell you that I've shot close to 1500 rounds in my 625 JM and the barrel didn't have any leading issues at all. Since I started reloading using Berry's and HSM plated bullets I haven't tried any in the 625 yet but have run about 300 through my 610 with not a bit of leading. For an absolute fact I can assure you that plated bullets will not present a leading issue in a S&W ECM barrel as long as they are properly crimped.
BTW, I only use a 0.002 to 0.003 inch taper crimp on my ammo. Testing with a bullet hammer has shown that bullet pull due to recoil isn't an issue with this much crimp because it takes a pretty good whack to get the bullet to move. Setback in a semi is also not a concern, testing the 40 in my Sig P239 and the 45 ACP in my Ruger SR1911 shows that it takes 8 or more rechambering cycles to set the bullet back more than 0.010 inch. Quite simply you really don't need a lot of crimp to lock the bullet in well enough for range use. Note that measurement is taken measuring the diameter at the edge of the casing and checked against the diameter about 3/16 inch back over the bullet, so the total taper is the larger diameter minus the smaller diameter.
As for the ammo you already have loaded, I would suggest using them in a revolver or semi that has a barrel with traditional cut rifling. Otherwise you'll be facing trying to lube the bullets externally sort of like what we see on 22LR ammo and I don't think that will work very well.
PS, the way to spot an ECM barrel is to take a close look at the rifling. If you find there aren't any sharp edges and it looks like it been over-polished and worn out it's an ECM machined barrel. The actual process is identified as Electro Chemical Machining by S&W and technically it's a variant of Electic Discharge Machining or EDM.
If you find your rifling has good sharp edges at the lands and grooves then it's most likely that you have some type of functional flaw in your revolver. Personally I would suspect a cylinder with UNDERSIZE throats and would use a pin gage to check the diameter. IMO you would like to see a 0.452 Minus gage just barely pass and not see anything under 0.451 inch that won't go in. I'll also tell you NOT to try checking your throats with calipers, it's not accurate enough. You should either use pin gages or ID Micrometers.