I guess that depends on what else you are trying to get out of the high country? I got all of my bucks meat and head/cape out in a 3200 with room to spare. I have a buddy who has done it in a Badlands 2800. So I would say with the 3700 you will be able to get all of your buck out and have some room extra for camp items. My 2 cents.
Although I haven't done it before I could fit a whole deer on/in my Badlands 2200 given that it doesn't have a HUGE body. In 2010 I packed two hind quarters and the head and cape from my buck along with my tripod spotting scope and other day hunt supplies... I know I could have fit it all in there had I boned it out, might not have been too comfy or have enough room for ANYTHING else but I coulda squeezed it all in there... So I know you could fit it all in a 3700 cu in pack with room to spare... IMO
I would say the meat takes up 1500-2000 cubic inches by itself. Figure out what your gear takes and add them together. Or you can put some of your gear on the outside of the pack. A 2200 will do it, but I wouldn't go much smaller.
How carefully are you guys boning a deer. 2 years ago I hauled out my deer in a Eberle Gunslinger which is like 2800 CI and my pack weighed ~70# (and was completely full of meat), my dad also carried a load of about 40#. This was boned meat with only a few tools, water, etc., as I had already made a trip out with my gear to meet my dad. I'm not trying to nitpick guys and how much they take or leave on a deer, but how much can you carry with a 2200 CI pack? I've hauled out 3 mulies and it's always taken me 2 trips (disclaimer: I'm a skinny weakling.)
In Colorado this last year my hunting partner and I used the Eberlestock J34 and they were great! They won't haul an entire camp and a deer without the spike duffel though. We did have room for a deer, a rifle, and extra layers of clothes.