How was payment made in the first place? Couldn't they just reverse/credit that way?
In theory, yes. The payments were made by credit card. The same card is still on file.
I actually put that question to them and they confirmed it would be possible. The CS person I dealt with on the phone was actually very helpful and tried to put the refund through directly to my card. A systems issue prevented her from doing so (it was in an old system), but she indicated another team would be able to do it. I was subsequently told the other team couldn't do it either.