Carry-on your meat.
Most airlines don't have a carry-on weight restriction (look it up before you book). I've twice filled my SG pack with meat and put it in the overhead bin. A SG bag will fit in a standard 737 overhead bin correctly, ie bottom of the pack perpendicular to the body of the plane. A boned out caribou or a boned out bear will fit in your bag. Freeze the meat solid, place it in a roll top dry bag, put the dry bag in your pack. If you max out your pack you can put meat in your "personal" item under the seat. I managed to get a caribou and a limit for salmon from Adak to Denver, with no issues. Also a bear from POW to Denver.
On the trip out put all your necessary gear in your carry-on, wear your boots. Knifes + optics, place in your rifle case. Fly direct it possible, you are much less likely to have an issue with a missing rifle on a direct flight. On the way home check all your clothing, it doesn't matter on the return trip if they lose your stuff for a couple days.