Restructuring part 2

This is the rest of the mega merge that brings master up to where my branch is. From now on things should be incremental.

I tried to do some tricks to make this cleaner, but I'm wary of using rebase (and I don't know if there's a policy about that), and cherry-picking changes didn't seem to be a great idea when there are so many. The tool can take care of handling the merges.