Tom Hargis taught me a trick to deal with releasing the load from a loaded gi-gi which should work for the reverso as well. The other answers given calls for releasing the weight off the bar biber. (the rope goes around this biner in both the reverso and gi-gi) Tom showed me a way to lever the device to make it horizontal, then it becomes a stitch plate and you can lower like normal.
Take a sling and girth hitch it to the lower hole on the gi-gi. For the reverso, girth hitch longer metal loop. (the one clipped into the biner when rappelling) Take the sling and pass it up through a biner in the anchor somewhere and clip it into the harness. Lean back and lever the device horizontal. Keep a grip on the brake hand and lower.
I've done it on the gi-gi but not the reverso. To feed out slack, I've moved the device horizontal by hand to pull out as much slack as needed.
These devices have an advantage if ever you need to lift a partner up a climb. I've had to do this but I doubt that you all will ever need to do this. Like rescue skills, a good thing to know. While belaying off the anchor with either the gi-gi or reverso, put small prussick on loaded end of rope. Put a biner on this prussik and it will become a weak pulley. Take unloaded end of rope and clip it in that pulley biner. Now you have a inefficient 3:1 pulley system. (probably a 2.5:1) It works good for when partners fall off on a steep climb and can't touch the rock to get going again. Or falling early on the second pitch of canary. I wish I could take credit for this but Tom taught me this too. Props to him.