I don't think a reinstall deletes the folders in your documents, where all your custom units are stored.
For example this headless problem only occured when I restared a game after loading one. (From which I learned is a big no-no right now as they are not clearing stuff when you quit a game yet).
When this happens does it happen after a reload or something like this? You should also check to see what custom units are in your folders as I think a problem might lie in the reading large amounts of characters in there. (I can get this glitch with as little as 5 sovereigns in the reload). I don't make any custom units, so I guess I haven't been able to check this out that way.
I will try to make lots of custom units and see if I can get this equipmentless (empty) character problem and see if that does it. This bug has me curious.