I would also consult another vet ASAP. How long has he been on Prednisone? Has your vet ever checked his blood sugars to rule out diabetes or kidney problems? As for the littermaids, have you thought of adding another old fashioned litterbox? Maybe he'd prefer the low tech solution. Finally...
I agree with gardenandcats - pick a high prize item to tempt him. I would also put new kitty in quarantine for a few weeks. Do you have a spare bedroom that she could stay in? Also, your shelter kitty may have (or may develop) a kitty cold from staying in the shelter. It's a common occurance...
