I wonder if--in the same way most browsers use a heuristic to block pop-ups if they weren't triggered by a user action--we could come up with an effective heuristic to do the same for pop-overs.
I'd think the simplest thing would be blocking "position: fixed; width: 100%; height: 100%;" curtain elements, along with anything that stacks "above" them. They only have two valid uses that I can think of: displaying lightbox-like image galleries, and embedding modal confirmation dialogs in single-page apps. It'd probably be easier to figure out a heuristic to whitelist these two uses, and deny everything else.