Whatever you do, you will need to take off the load from the tuber in locking mode. So I'd use the same technique as when going over a knot (well there's probably more than one technique for that, but this is the one I know and use (luckily for training only till now)), just adapted to the ascending setup you are in:
Take a cordelette and make a prusik (or blocking knot of your choice) just above the ATC/tuber leaving one end rather short and secure that end (double fishermen's). Then attach the other end to a biner on your harness with a Munter hitch, which you then secure with a releasable blocking knot. Then use your blue loop to get load off the tuber and pull on the upper shackle of the tuber to let rope go through until your weight rests in the newly added cordelette. Now attache your usual backup prusik for abseiling below, also getting some loose rope up to work with. Then change the tuber to descending mode. Once all is set and double checked, release the blocking knot and lower yourself with the munter, until the load is in the tuber/backup prusik. Then remove the cordelette and start abseiling.