Hogue, or any similar, is a really good suggestion
if the shoe fits, wear it, don't worry about looks
mostly I suspect that exposed backstrap is unfriendly for OP, leastways with a 125 gr wt 357 load, or could be his grips are not true perfect flush tight fit at backstrap, have seen some aftermarket panel grips that didn't cinch down completely tight/smooth at backstrap, and that is pretty critical no matter what made of
just trying on a shooting glove, (most any non-slippery glove from wallyworld would do, cutting off glove trigger finger optional), would be a quickie way to find out, paying close attention to how your hand feels before stacking up a high round count
if the glove works out, then could hunt up some other grips of choice for the gun
ultimately, it could be as simple as putting a little more "handle" on it