Flatlander....I'd start by calling some local meat processors where you will be hunting. Here are some ideas I have used in the past.
1. Some meat processors will cut meat and donate it to charity. Often you have to pay the price of the processing.
2. If you want to bring some or all of the meat back, have it cut, wrapped and frozen in Wyoming. A lot of processors are geared to get the meat done VERY quickly during hunting season, but you should locate a meat processor ahead of time and call ahead and see if you can expect a 1 or 2 day turn around. Once the meat is cut and wrapped you can carry it as luggage in ice chests. An elk can fit in 5 or 6 ice chest that would be 50 pounds each or less. If you have more then say 8 hours to get the meat on the plane, I would put dry ice in the ice chest to keep the meat frozen solid. You cannot have dry ice in your luggage at check in, so you will have to get rid of it before you check in. I've always had a rule of thumb that solidly frozen meat will travel for 24 hours in an ice chest without a problem. A cape can be frozen and carried the same way. Some meat processors will ship frozen meat, but you are talking overnight shipping costs, or refrigerated truck. As far as the antlers and cape, years ago, antlers were split at the skull so they could be placed together to reduce the bulk, then wrapped and taken as baggage (the taxidermist can repair that in the mount). Not sure if that is kosher any longer. What I did with a New Mexico bull a few years ago was to locate a taxidermist ahead of time and have him mount the bull and ship the mount by freight. Taxidermists do that all the time.
3. You could have the processor make dry type sausages (salami, meat sticks, etc), and jerky that would not need refrigeration, and then ship that by regular UPS. Since that type processing takes some time, it may take a few weeks until your meat is shipped to you.
Again I would call a meat processor where you plan to hunt and explore the options.