Is there a category for Coop (either whole or Art Therapy) that is glitchless? It looks to me like all the top speeds use glitches like high ping floating and pressing down cube buttons without actually putting a cube on it, etc.

There are currently no glitchless category for coop nor single player. As aspect said, you can submit your run in the normal coop category. You won't be able to get the world record, but no one gets the world record first try ;)