I don’t like to be the wet blanket, but I don’t think there’s enough spares in inventory to ensure a less than 2 week turnaround for component replacement or whole unit ( transfer case ) replacement. There’s been 2 or 3 fairly well publicized transmission failures documented on FRF and they were closer to a month. I’m not saying that’s right, I’m saying that might be closer to reality.
Also, Ford isn’t going to mech replace a truck with any significant miles on it - literally, if it didn’t stop working within a block or 2 of the dealership on the ride home, that’s off the table. Keep in mind, the dealer “bought” the truck from Ford, you in turn bought the truck from the dealer.
If you financed and you financed through Ford Credit, you could have a legitimate claim for them to credit you the amount if the truck is down for more than 2 weeks. Keep in mind, if they compensate you; that is, provide you a loaner, or pay the monthly payment for you, that could jeopardize a subsequent lemon law claim in court, if it ever goes that far. state laws vary, and you are not there yet.
That said, I would definitely be pushing for something, given the circumstances, but until or unless you pass a month of down time, there is no financial interest for the manufacturer to entertain the concept of a vehicle replacement.
Your best bet is to keep the dealer on your side as an advocate. Be understanding beyond reason, be engaged, but not a pest. Be courteous to everyone you meet at the dealer from the lowliest porter, to the owner and everyone in between. MAKE them want to help you because you are a super nice guy. Don’t even suggest legal moves, don’t try to threaten or hold anything over their heads, just deal honestly, forthrightly and get as much in writing or - if legal by the circumstances, recorded. Make your plight personal to the dealer who is repairing the truck.
IF things go really, really south, then seek a lawyer’s help / advice. Here’s what I would suggest. Have a private, one on one conversation with both the mechanic and service manager. Tell them in no uncertain terms that this is not for attribution, no quotes and anything said is 100% anonymous. Ask them point blank - what can you do personally to help drive the issue to resolution as fast as possible. You know you can’t change physics, is there anyone to contact, who can help you all get the repair done fastest?
A lot of times these people know who the right people are and deal with them frequently but the customer either has to ask or have a significantly compelling reason for an “escalation”.
It’s easy for us here on the internet here to be detached from this, we’re not the ones impacted by this. I’m not meaning to preach to you here, but try your best to keep a level head look at the big picture before taking any actions.
Good luck..