Dave and I put our heads together and then we sat down with Nathan to come up with a strategy to get things back on track. We've identified one of the key issues is that he is embarrassed and worried when he has an accident, and thus his instinct is to hide it. So we put together a plan to deal with that:
If he does a BM in the toilet: he gets the Xbox for the rest of the day
If he has an accident and tells us or tells us the truth when we ask: Xbox for 15 minutes
If he has an accident and lies: he loses the computer and iPad
Clean all day: $ 1
We're going to have to monitor this carefully. After he has a week or two of success, we'll have to mix things up to avoid getting trapped in the same situation again.