DF, it dang sure aint going to hurt anything. I'm running several HS stocks, some bedded and some not. They seem to shoot well either way. I had one that shot better afterwards, but most all of them have shot just dropping them in. You can feel the movement on the bbl if the fit is bad.
Let us know how the new rig shoots. That's a very interesting cart IMO.
Good Luck
loder
