I put a synthetic stock set on my 06 handi, which lightened it up by an appreciable amount. But it made it even more of a shoulder-smacker off the bench. It's on the ragged edge of what I am comfortable shooting, recoil-wise. And mine jumps around on a rest too.

I can't remember what the last load I worked up for it was, but I'm pretty sure it was with Hornady 168 grain bthp match bullets. It would put the first two really close together, then a third one would be out an inch or two. Plenty good enough for me. Odds are I wouldn't get more than two shots at a deer with it anyway.