@buckshot85 to answer your question, there are 4 permits required with USFWS potentially that do not apply to you. Leopard, Lion, Elephant, and Rhino require USFWS endangered species import permits. The permit applications ask a question: A.) Where are you going to hunt it, or B.) Where did you hunt it. Nobody sane gets pre-approval for option A because they could sit on that permit for years and by the time you get it, that area is not in play for hunting anymore, the operator closed, the PH retired, etc.
Regarding your baboon, I don't think you understand the magnitude of costs you will endure. This is in no way belittling a working man but rather advising you as a friend how F'd you'll be trying to import just a baboon. Just to clear US customs is a $500 charge.
The USDA permit required for primates and swine adds another surcharge, that's the additional headache, additional customs inspections, and additional delays that can be added to getting your crate of trophies home to America. The airfreight to get things to the States right now is up 400-800% since Covid...you'll pay hundreds and hundreds of dollars for the freight. Also, there are freight-forwarders potentially getting it from taxidermist to the major port. Then there are in-country permits and fees.
When you get it home, even if just a bleached skull and a salted hide not yet taxidermied, your cost to get one baboon to the USA is going to be in the $1500-$2500 price range.
Now if you're adding in many other animals, the fixed costs stay the same and the variable costs only add a small percentage. I think to ship in 15 animals from Zim pre-covid that were very, very heavy, plus taxidermy, I was into it about $11,000-$14,000 all-in. On another shipment of just horns and green hides I was all-in about $5000-$6000. These are pre-covid numbers.