Around 11:30, I headed for San Jose and presented my ticket and paperwork to the Amtrak station agent. This time, the agent didn't claim that I owed them $1900. She could see the record, and that the car number on my reservation had been changed, and that I owe nothing for it. But she couldn't print it. Nothing she did worked. She got on the phone to someone else at Amtrak, and they tried all sorts of things, none of which worked. In desperation, the agent hand-wrote my new car number on the old ticket and gave me a printout of my reservation. The printout, however, very prominently says THIS IS NOT A TICKET. That being the best I was going to get here, I headed for my office. It's possible that I should have called AGR right then, but I was already taking way too much time away from my office -- I was gone for two hours total from the time I signed off this morning to the time I got to my office.
After lunch, I called AGR and, after explaining the situation again, was once again sent to second-level support, as I'd told the first-level person she'd have to do. The second-level agent said that this was sufficiently complicated that she'd have to make some other calls and get back to me. After an hour or so, she did.
The problem here appears to be that the Amtrak ticketing system is set up in such a way that Amtrak-the-train-operator isn't supposed to be able to touch Amtrak Guest Rewards tickets and vice versa. Their systems touch each other at certain points, but there is all sorts of interlocks to prevent changes. When, for operational reasons, my reservation in car 4911 was moved to car 4910, it created a logical contradiction. An Amtrak agent wasn't allowed to print the ticket because the system said "ticket already printed." She couldn't void the ticket and print another one because the system prevents changes to AGR tickets.
The solution that Amtrak Guest Rewards came up with was to simply cancel the entire trip (MTR-SDY-CHI-LAX), all three legs/six tickets of it, and create a brand new reservation record, with all of the same details but a new reservation number. That new reservation number hasn't been printed, so I should be able to go to an Amtrak Quik-Track ticket vending machine -- like the one in Fremont/Centerville -- and print the new tickets, which replace the old ones.
At Lisa's suggestion, I will keep the old tickets and take them with me, stored away in case there's any further questions about this.