You cannot carry-on a bow, arrows, knife, or broadheads. They must be in check-in luggage.
Lot of other good advice here.
When I fly and meat is involved, I mostly use two of these for my check-in luggage
http://www.igloocoolers.com/Coolers/All-Coolers/60-Quart-Ice-Cube-Roller They can store all my equipment on the way there in them (take down bow) and they work well as rolling luggage when negotiating the airport terminal. I DO put a packing strap or two around them to keep the lids shut.
I also include "garbage" bags and an expandable gym type bag in there too.
On the way back I mix the frozen or iced-meat (yes iced, not frozen as it wasn't an option). I mix the meat and my bigger gear (i.e. bow etc) in the coolers protected with garbage bags. The remaining stuff (mostly clothes) goes in the gym bag as a carry on. You should be able to keep two deer and all your hunting stuff in the coolers and keep them under 50s# each. Seriously boned out deer are not that heavy.
Another idea is to take home the "good" cuts of meat and find a butcher to take your scraps to have sausage made and shipped to you later.
Another trick I have done is when I needed a sleeping bag to stay in a bunk-house is to go to a walmart at your destination and buy one for $10-$15 and leave it there. It feels a bit wasteful (to me), but it is really cheap and saves lots of space.
BTW...the ideas I suggest are not for fly-in hunts and such. This just works for hunts like you are taking that requires commercial flights. Good luck.