I have never flown in anywhere for a bear hunt, but have for deer and have a little experience with your taxidermy question.
Getting the meat home is pretty easy. You can take your gear out there in a cooler as one of your checked bags. If successful, put meat in cooler(s) and check it as a checked bag. You may have to work out something with a meat locker or motel with a freezer before your flight where you can get your meat cold or frozen. The gear that is now displaced gets shipped home via USPS or whatever service you prefer.
We went through the taxidermy question this fall with antelope. We left the head and hide out there and had it done, then shipped it home. It added $150, but took away stress of taking care of it on the two day trip home. Plus the taxidermist we used is much better at antelope than what I can likely expect at home. No regrets there. Research taxidermist in the area, talk to them and get a feel for how it would work. I about guarantee it's not their first time dealing with it.