Since I was working in the Admin section, and I mentioned uploading new versions of the module, I figured I should go implement that functionality.
Our end goal for this is for the system to automatically ping the official release server, download new versions when they're available, and prompt the local sysadmin to do a one-click install once they're in a position where a little downtime is acceptable. Unfortunately we need to do more work on the moduledistro module before we can get there.
For now, here's a quick implementation that lets you do a file upload.
Conveniently I got to fix a little bug along the way about not being able to put a @RequestParam annotation on a method parameter other than the file one.