Agree that you need a service center in central NM! Have a friend in Albuquerque who might someday be interested in a Tesla.
Dead in garage happened to me twice, except that the 300 mile tow was to Littleton CO. The first time was the infamous MCU failure, under warranty. Since the mobile service ranger didn't have a replacement MCU at the time, he brought me a rental car (Enterprise) and took my car to Littleton on the same flatbed trailer. I drove the rental to pick up my car. No cost because it was under warranty. Don't know if they are that generous nowadays.
The second time was a completely dead in garage — couldn't even unplug the EVSE — out of warranty. Tesla roadside quoted me a tow cost from a local company of $1400 and suggested that I check with my insurance company. I called State Farm and they verified that Littleton was the "nearest place the car could be serviced," then arranged for the tow and took care of it. At no cost to me, not even a bill. I was pleased, to put it mildly.
When my car was ready for pickup I rented a car (Enterprise) at the nearest city, to drive to Littleton to pick up my car. When I told Littleton service that I had done that, they picked up the cost of the rental (Tesla still had a deal with Enterprise, don't know if they still do). Even though I was out of warranty!
So, my take is that Tesla service has (or had) some discretion on how they handle those long distance repairs. YMMV.