Ok, got an update. I talked with the operations manager at the servicing dealership today, and he has, by far, been the most helpful person in this process.
He gave me the rundown on what Ford will cover with the trade assist program, and I also asked for his 2 cents on what he'd do if he were in my situation. He's worked both for dealers and for Ford corporate for 20+ years, so he knows the system pretty well.
Basically, the trade assist program would allow me to trade my existing raptor into a dealer in exchange for a new raptor, and Ford would provide that dealer with an extra lump sum of cash as an incentive. Given that my raptor only has 1100 miles, it would still be a very appealing trade for many dealers, and they'd likely be able to sell it used at near original MSRP. With the lump sum of cash, that would be a few thousand extra bucks in the pockets of most dealers. That said, I'd still have to find a dealer that wants to work this out, figure out transportation of the truck(s), and go from there.
The servicing dealer's recommendation was to take the existing truck back and ask for an extended service plan from Ford. He also said that the 'trade assist' program is typically offered for a year or two after it's first documented on a customer's case, so if I really hated the truck after driving it for another couple months, I could still trade it in. Finally, in the worst-case scenario, I could pursue the lemon law route if the truck was repeatedly in and out of the shop in coming months.
According to the servicing dealer and every mechanic I've talked to, the transfer case is not a difficult fix, and it's unlikely there would be any additional issue after the repair. It's a pain in the ass that it happened this way, but it shouldn't be an indication of things to come. If I do continue to have issues with the truck, it's all covered under warranty, I still have the option to pursue a Ford-assisted trade, and I could go the lemon law route if I really needed to.
All things considered, I think I'll take my truck back and hope for the best. If I have more misadventures, I'll go from there. Thanks for the support and help everyone. Hope to have the truck back home in a couple weeks. I'm excited to rejoin the raptor crowd!