Wow! I've never heard of anyone paying for usage under the lemon law- but I don't know much about it. If after this attempt, if things don't get resolved, I would seek legal advice and learn how lemon law works in your state. They probably don't want to buy ANOTHER one back.
If you do wind up taking the journey to Utah, (pun intended) please make sure insurance is up to snuff, you may have to cover yourself for that trip. I know I would.
I am working through a similar no shift diagnosis my self, on one of the F550's I work on.
I happen to know this unit was abused last winter, and now during our summertime prep for next winter, I find that the transfer case shift motor won't shift the case out of 2 wheel. This is a current gen truck with a Ford case. When I remove the motor, and let it hang, it works, and if I attempt to move the nub with a fits all, I got high effort but it shifts. The decision makers want to try a new motor, and I'll be putting it in next week, but I think I'll be going in the case.
Why can't they just leave at least one work model full manual, like Dodge?