maybe just "if velocity < 0.01, find which side is closest to the floor, and if its within 1mm of the floor, take the opposite side (the one facing up) as the answer"
The only edge case I can think of is if it gets close to balancing on an edge, and then finally tips over to one side or the other. But in that case I don't think the face closest to the floor would be within 1mm of the floor, so it should still work.