Hello, FUD. I've never shot an alligator so this is just opinion. Based on the two calibers you mention, .357 or .45 Colt, I'd go with the latter. Since alligators cannot sue you in civil court if they survive, handloaded ammo is viable. I'd go with a Ruger and "hotrod" the .45 Colt using at least a 250 gr hard cast SWC with sharp shoulders. Expanding ammo, even XTPs, could possibly expand more than we want penetrating
the scales, etc on the alligator. I know that in "hard target" penetration, the JHPs do better than expected, but I don't know if these scales are "wet" inside or not. As I said, I know little about these big reptiles.
The .45 Colt with at least a 250 gr CSWC moving at say 1200 ft/sec should knock a big plug out of the 'gator(s) and give deep penetration. Probably the .357 with hard cast SWCs would work fine as well, but it just won't be cutting as wide a hole. Anyway, that is my admittedly uninformed opinion on your dilemma. Best and good luck.