Inbox me if you want rental truck info and I'll give you a quick run down of how I'm going about my Idaho bear hunt this May and why. I air travel west from the east coast. Not willing to lose hunting time by driving.
Otherwise just know people tend to make a much bigger deal out of flying with meat than it actually is. It's just luggage. Period. Pre-order waxed cardboard insulated 50 lb 'fish boxes' and any other processing supplies you can think of from the closest Walmart. Pick it up if you kill. Cancel if you don't. I've bought a small cheap freezer in a pinch before but lining up a processor to do final cuts, packaging and get it frozen is a better idea. Just your worst case scenario is $150 freezer or renting an Airbnb for a night (hard to plan the date as you don't know when you'll kill).
I'll probably pay a local taxidermist to send my hide to the tannery then have tannery ship the hide to my taxidermist depending on what it is and what I want done. Probably wouldn't make sense to do that with a rug, but it could for a half mount. I just paid about $400 to have an axis shoulder mount shipped from Sante Fe, Texas to NJ via FedEx for a ballpark. This includes building the crate which wasn't expensive nor free.