Have you heard of those automatic litter boxes?? I have heard that they are wonderful. He will do his duty and as soon as he is finished the sifter will remove the waste. So your kitty will think he has a clean box everytime. The only drawback is that they cost like 100.00. But for this case it might be a good investment.
Good Luck. I understand with the attached thing I have a hard time with that also!!