Thank you, Shannon!
I am really impressed by how quickly you sorted this all out, and I'm glad that my posting will actually help make things clearer for everyone (passengers and customer service folks).
Thanks to being able to put my call on speaker, I was able to keep working while I was on hold, so it wasn't as bad as it might have been (this is a strategy I recommend to everyone facing a long hold). The good will of the people I spoke to was so apparent, and the confusion was so honest, that it was hard to get upset. They really were trying their hardest.
I really wish that I had taken their names, because they did everything they could, given the circumstances. If you think that the names might be noted in the record, PM me and I can give you my information.