If you removed the plastic on the door, you could probably fit the bucket on the floor so its not teetering on the ledge. On my fridge it was just held on by like 20 screws, took them off and rescrewed the weather stripping back on and it holds its temps like a champ. The foam behind my door was hard though, so if yours wasnt you might have to fashion a cover.
I also build an STC-1000 in an evening watching the above posted video and one other one, I put a mini ceramic heater in it for heat, the heater sits on the back ledge just fine. I'm starting to think it gets it too warm too fast in there though, so by the time the bucket gets up to temp its like 80 degrees ambient air and then the cooling kicks in and i'm going to be swinging back and forth on temps a lot. I will need to do a test run with a bucket of water and monitor it, the next step would be the heating tape as mentioned above as well.