I say, "why in the hell would someone want to carry a snub revolver in .357, particularly an airweight version!?".
I was shooting both 158gr. and 125gr. factory loads out of a stainless K-frame with 2" compensated barrel and those bastards hurt! There's just no way even a minimally experienced shooter can control a J-frame snubby in a self-defense situation.
You're right, they kick some. I have a 3" barreled S&W 60 J frame with adjustable sights. It is a mean spirited little SOB with an all around nasty disposition. A cylinder full of full power ammo in a day is about 3 rounds too many. On the other hand, the little rat is accurate. It thrives on the 125 grain federal full power .357 load typically holding pairs of shots ... from a rest of course ... within 2 inches of each other at 50 yards. It is not a fun gun to practice with but it is a real confidence builder to carry. Sometimes a portable but brutal gun that puts a very few shots exactly on target is more useful than a less portable gun that comfortably puts lots of shots in the general area. YMMV, but for me, it's the ultimate "pack it a lot and hope to [bleep] I don't have to pull the trigger" gun.
I have not handloaded for specifically mine and probably never will. Most of my .357 handloads are for heavy framed guns. The little J frame ... and my hand ... probably would not survive. My current TC, and the last blackhawk and last gp100 I owned, all liked the same thing: 17.5 grains of 296 under a 158 grain hornady XTP. I'm very careful to be sure nothing but fresh, factory Federal 125s or .38 wad cutter ammo ever get into the J frame.
If it didn't like that Federal factory stuff so well, I'd give Remington's mid-range 125 grain .357 a try .. golden saber, I think they call it. Still in production? Dunno. It's not worth shooting that gun enough to find a different load, just feed it what it wants and leave well enough alone.
Tom