I agree with your general categorization! I'm on board with AUs where we're still in the same canon but something has changed (including the AU of Everybody Lives/Nobody Dies, obviously), but I don't really get fics where the setting has *completely* changed. I've done it rarely (I can think of two cases where one was my idea and one was by request) but I've worked hard to keep as many elements and the relationship types the same as in the original canon, otherwise - how could they possibly be the same characters if everything in their environment and background is different?!

The one missing item from your list, I think, are crossovers, where we squish two fandoms together. I see those way less these days than they used to be, but in those cases authors usually seemed to retain elements from the original canon and just tried to weave them together. That could have been more my circle of fandom friends though!