If you can get the meatprocessed and frozen would be the first step in getting any of it on a plane with you. Otherwise, plan on having it shipped back to you at a later date. Also might look into having the taxidermist work donelocallyof your hunting destination and then have it shipped back to you when finished. This won't be too cheap if you have a shoulder mount 6x6 elk, but more convinient than trying to take a large rack through an airport.
If you kill early enough and are lucky enough to get it processed in time to freeze it before youfly back home, then taking it back as checked luggage is the cheapest way to get it home. You can think about shipping your hunting gear by way of UPS instead of flying home with it. So your meat would be your checked luggage, and your luggage would be shipped home by way of UPS.