Not sure what all crossing state lines with livestock entails but horse people who show their horses do it all the time. Can't be that involved. Probably something like showing they've been vaccinated.
Taking stock into the backcountry is a hassle. I use a couple mules and also hunt solo. Strange things seem to happen on the trail. One gets away from you and heads off without you or decides it's not crossing an obstacle. You have to get up early to feed and water them, twice a day. You will likely have to pack in their food before the hunt unless there is somewhere to graze them, which there usually isn't. If you do graze them, that takes a lot of time too. Training is a big time commitment and with wild burros, it's probably double or triple the time/effort of a domesticated one. Equines aren't like dogs. They're not really good company although burros are said to bond better than horses. As far as traveling with them, horses once trained travel well although you might need to have an in-between spot to overnight. It's a long term commitment that makes zero financial sense.
That said, if you get an elk down, it's hard enough getting yourself out let alone the meat. Taking stock in is a lot of work but you'll kill yourself boning out and packing elk meat by yourself so for that reason, it's absolutely worth it. Oh, and it's just cool too.
I started my animals from colts. That was hard. Nothing wrong with getting a good broke animal and remember, the purchase price is usually always the least expensive part of owning horses/stock.