If you are having it shipped home by a butcher/processor/shipping company, it will be very expensive.
Due to the weigh of the meat, the time frame in which is must be delivered, and the distance its covering this can be one of the most expensive parts of a hunt. Most of the time the meat is processed, frozen, packed in foam cooler inside of waxed cardboard boxes, and shipped via airline / overnight or 24 hour delivery. Same can be said about the trophy
I have flown home with meat and trophy's before and much prefer it than shipping at a later date. It is cheaper to pay the excess baggage few on a few coolers and have your trophy wrapped up in a duffle bag (or have a taxidermist handle the Euro mount and ship it too you, that may be a more cost effective option).
I try to reduce the amount of gear I am flying home with by shipping clothing and other small/cheaper items home via fedex/post office. That way I am only flying with my weapon, valuable gear, and meat/trophy. I have even brought a small cooler along with my backpack on to the plane as my carry on item that was stored under the seat infront of me, it contained my bulls backstraps and tenderloins (it wasn't leaving my eyesight).
If I was you I would do the following if successful:
- Have a processor cut, package, and freeze your bull
- Leave trophy with taxidermist for Euro or skull cap and wrap in duffle bag
- Ship home hunting gear if you are leaving trophy with taxidermist, if bringing trophy home just bring gear in same duffle and carry on backpack
- Pack as much gear into your gun/bow box as possible
- Assume on 200-250lbs of processed meat from a bull elk, buy coolers out there, pack 3 coolers with 70lbs of meat (above 70 lbs the overweight fee goes from $100 to $200) + your small carry on cooler with the remaining.
- If you are not flying home the same day you are picking up your meat, have the butcher put some dry ice on the top of the meat with some newspaper or carboard. This will keep the meat solid.
- Once at the airport, you should only have your gun box, coolers, and carry on backpack. At check in you will have to pay for the additional and overweight baggage fees (below is off of American Airlines):
- 1st bag: gun/bow box is $25 or free most of the time
- 2nd bag: 1st cooler is $135 ($35 for 2nd bag and $100 for overweight)
- 3rd bag: 2nd cooler is $250 ($150 for 3rd bag and $100 for overweight)
- 4th bag: 3rd cooler is $400 ($200 for 4th bag and $100 for overweight)
All said and done you are looking at around $800 in baggage fees, with that said you could drop the 3rd cooler and that would cut the cost significantly.
The shipping costs to the East coast that I have seen are anywhere from 1,200+
All of the above headache is one of the main reasons I just throw everything into my truck and drive out for Elk. The fuel for driving out and back, hotel room cost, meals, etc is under $1k and is usually a lot cheaper if you travel with a partner to split the costs with.