UPDATE: On February 4th, we received a check for the full amount in dispute. It was a bit of a pyrrhic victory considering how much time it took to get resolved, but in the end Amazon did the right thing.
UPDATE: Amazon contacted me to tell me the check would be returned and that to be safe I should also have my bank do a stop payment. Kind of ridiculous to make such a suggestion given that the check has already been cashed! And I wonder how they plan to return a check that's already been returned, (by virtue of it being cashed). I know they're powerful and all, but still.