You hoping to fly back before the meat is done with processing puts a wrinkle in the obvious possibilities. I've known several hunters who gave up their entire cooler of meat in exchange for local assistance in initial processing , packing and shipping their cape, hide, horns, etc.
I like to pack my boots and heavy clothes, extra gear, etc. into a 44 quart cooler with my name and address written on 3 sides with a big marker, with a TSA -approved locking luggage strap around it, through the handles. Its an affordable baggage fee and nearly indestructible. If I get game on my trip, I de-bone the meat then have it minimally processed, wrapped and flash frozen in the deep freeze. Most processors can do this for you in under 24 hours. Then pack it in my cooler, put my boots, clothes and gear in a duffel and pay the additional bag fee. The alternative is to have your meat shipped to you in a styrofoam cooler inside a cardboard carton a la Omaha Steak Co, via UPS express.