1.375" to .5" is a huge jump, and if you could get to this point, then it would be worth your time....although I'm betting you're not going to reach this point with your rifle, most factory hunting rifles are lucky to touch 1MOA, let alone .5MOA, 1.375" at 100yrds is a pretty good group, I'd like it down lower towards 1", but there's nothing wrong with it.

As far as practicing snap shooting goes, it's a waste of time as well, if you've got to swing and take a relatively blind, aimless shot at a deer, you're not doing your part in the first place...yes it's handy to be able to snap shoot in the event you get rushed by a bear or something, but that doesn't seem to be the point of your case.

Taking snap shots is at best border-line on being unethical, if the majority of your shots are snaps, you're not hunting, you're walking around until you scare up a deer and winging a shot at it and hoping for the best.

Practice how you will play, if you're going to be shooting out of a box blind and have the ability to use sandbags, then practice from a bench is viable, if not, then practice position shooting, i.e. standing, kneeling, sitting, and prone...buying a good set of shooting sticks or a bi-pod can really help with this. I have a two position bi-pod on my hunting rifles, and a telescoping cane for support on standing shots, I also practice shooting all four positions free handed.

Remember what your group size is for each position and with or without supports, shooting 1" groups at 100yrds is relatively easy given the right conditions, but for most people the right conditions don't include off hand standing, it's quite difficult to shoot 2MOA at 100yrds unsupported and standing, especially if you're holding a hunting rifle! You're going to notice off hand standing groups somewhere along the lines of twice-four times as big as your bench rest groups, hunt your quarry accordingly.