If only I had know about the Amex moving offer...
I have mainly used Diners Club and, where that was not accepted, a very simple VISA card, so far. VISA doesn't seem to care at all and Diners Club is not issued in Canada these days. (And acceptance is dismal. Which is especially strange as Diners Club is owned by a Canadian bank, eh.) Plus, I talked to Diners Club and they don't seem to have any service for people moving.