It looks like we won't have to fight for this after all.
I got a pleasant surprise yesterday when my wife called to say that the service manager called her and said that one of the employees who worked on our vehicle showed up for work early, with a guilty conscience, and admitted to accidentally damaging our door.
My wife said that the manager was the most pleasant he's ever been when talking to her too.
He said that they are still backlogged with repairs for the hail storm months ago, but he'd do his best to make sure we didn't have to wait long. He said they wanted to get our Escape in as soon as possible to make sure there was no structural damage and to prevent the damage from getting worse until they can repair it.
They're willing to drive from the east end, to the west end where my wife works, pick up our Escape, drive it back to the east end to do whatever they need to do, gas it up, and drive it back to her work when they're done.
While I'm really happy with the way this is going, the pessimist inside me is hesitant to heap praise on them. I'll give credit where credit is due once this is all over. But for now, this is a huge step in the right direction.