I ended up transferring them to another registrar.
Today, I get a notice from the old registrar that my domain name renewal did not go through, because the domain name could not be found. And, they gave me a credit, to my account, not my credit card, but maybe I'll see about getting it applied to one of the few domains I still have remaining with them.
They also cleared out all the other domains that were previously still listed in my account, but had long since been moved to another registrar.
Weird.