by Ray Morris.
To directly address the OPs problem in a practical way, you might ask if you, Curtis Fornadley, would be allowed to indvidually contribute code from home. In that case, only patents you personally control would be affected.
UCLA would have the same rights either way, since it's a derived work based on Moodle they have GPLv3 rights either way. Owning the copyright on the derived work has basically zero legal affect since it's under GPL. They would let you retain the worthless "ownership" personally so that you could contribute it personally.