We just did this. Tried and tried to get tickets to Last Supper before we went, but couldn't. I found out that the 'old' reservation company has been fired and they had taken reservations for Sept and Oct and would not give their bookings to the new company. So they can't make any new bookings because they don't know what is already booked. They can take reservations from Nov 1 forward.
We booked the Milan tour (including the Last Supper viewing) with a company called Zani Viaggi. It was about 50 euros and 3-4 hours and I think everyone on the tour was there only to see the Last Supper.
http://www.zaniviaggi.it/tour/elenco_tour.asp?id_tipo_tour=1
It's the Gran tour of Milan. The tour was booked, but we were luckily able to get on at the last minute due to cancellations.
I mistakenly thought that we would be able to get Last Supper tickets at the church from cancelled bookings. We were told that even if the people didn't show up, they were already paid for and couldn't be resold. "I have my money - it's not my problem."
I suggest you book the Zani Viaggi in advance if you really, really want to see the Last Supper.