In my opinion, there are three 38+P loads that are reliable performers in 2" barrels, and an extra 3/4" can only help.
1) 158+P lead hollowpoints, also known as the LSWC-HP+P. These are commonly available from Winchester, out of production from Federal (which loaded 'em wimpy anyways, so no loss) and can sometimes be found in Remington boxes (these latter are reputedly a hair hotter than the Winnies, but not by all that much). Cor-Bon used to make 'em too - if you can ever find 'em at a gun show or whatever, snap 'em up!
These are an "old school" load used as far back as the 1930's, and are sometimes referred to by the name of agencies that used to use them: "Treasury Police load", "Chicago Load" and "Metro load" are three I've heard of. Not high tech, but they punch deep and generally expand.
2) Gold Dot 125grainers in 38+P flavor: a number of companies load this in addition to Speer/CCI: Proload, Georgia Arms and Black Hills. Probably more. All three of the latter have excellent reputations.
3) Winchester 130grain +P Supreme: has a real monster of a hollowpoint cavity, great example of a "tuned for the purpose" projectile.
In your gun, recoil and noise will be controllable, but effectiveness will be all you need if you plant 'em right
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In my opinion, too many other 38+P loads fail in 2" barrels. Granted, yours is a hair longer but...why risk it?