The next challenge became: could I get on another flight.
I called British Airways and the guy said that because my travel had started, he couldn't change it and I'd have to go to American Airlines whose delay caused me to miss the flight to make alternative arrangements. I explained the two tickets were unconnected but the BA guy claimed AA would still have to take care of it.
As the American Airlines ticketing staff had left for night, I spoke to the baggage department. They looked up the tickets and said, no, there's nothing they could do about it.
I called BA again and got another person. They said my "no show" counted as a cancellation but he could overlook that and let me change my flight.
However, when he priced it, he said it would cost $2,500 to change to fly the following day.