Lisa said, "Oh, wait, it's probably easier to get things out this way," and walked around to the back of the van and opened the rear door.
I stood there dumbfounded, and then I picked Lisa off her feet in a big hug. "You fixed it!"
She had indeed repaired the rear door. She carefully was able to remove some of the rear upholstery and work a probe into the door latch, which after some trial and error (helped immensely from having been able to work on a similar door assembly at the Pick-N-Pull last weekend) opened for her. With the door actually open, removing the access panel and replacing the door handle with the one we picked up at the junkyard was pretty easy, Lisa said.
Lisa showed me the handle she removed. The mechanism is held together with a rivet at its center, and that rivet was gone. We assume that it broke off in the cold in Tonopah and is now sitting at the bottom of the inside of the door, but there's no reason to go fish it out. When the assembly fell apart, the handle could no longer lift the latch on the door.
The rear doors on the Astro now work properly, and that's a big relief to me, because we need that access in order to haul the Match Game SF kit to Portland for Westercon. Furthermore, it's much easier to use the vehicle when we have rear-door access, particularly on our long road trips like the planned trip to Kansas City for Worldcon this year.
Lisa was very pleased at how she surprised me.