Yes it is a Premium extended warranty for 7 years or 125000 miles.
I’m not trying to be thick but - just to be clear, this is the FORD ESP, not an aftermarket warranty?
If so, as FTO said, something isn’t right.
If it’s an aftermarket warranty, I’ll bet that is the delay. Either way, the repair, such as it is, has pretty much lost its profit, and it sounds like at this point every minute they spend on it the dealer is paying for with probably nothing left coming from Ford. Maybe - that seems to be how the dealer is acting.
You really should have an appointment with this stealership management.
‘One is right about the numbers, the 10R80 is the modern TH400 or C6. It’s ubiquitous. It’s bad and nationwide. If there were widespread problems, it would be national news. This is one reason Ford is slow to make changes to the F series and changes are usually evolutionary. This is the big money maker for the company. There have been units that did the crazy downshift on the highway, not disputing that or making light of it and a lot of folks complain about the ‘harsh’ shifting and a few other failures but by and large, I’d bet we have more busted moon roof tracks than 10R80’s.
None of that helps you though. Were I you, I’d set up an appointment with the GM at the stealership to see how they can help resolve this for you.