Thank you for the context of the place import. 

I don't know if a tool already exists, but I agree that it should be possible to do it in a more automated way. I used the balloon tool to create the geometry and replaced an old way per closed loop of the relation to preserve history. Then deleted the excess ways and the type tag needs to be deleted. All of which I think could be semi-automated.

Modifying relations tends to be much easier in JOSM. I don't expect you to go back and change them all or anything like that (especially in ID). It should make it easier to map using simple areas in your future contributions.