Any chance you can give him a deadline and then tow the car back out of there if it's not done? Then he has a transmission sitting there that nobody is going to pay for, so surely it's in his best interests to get it done.

When we had our camper repaired earlier this year, they had it from the first week of Jan to the middle of Feb, with no communication as to when it was going to be repaired. We started to hassle them every day in the end and they were so sick of it they got it done. But then they took our money and wouldn't issue an invoice. I went to consumer affairs and found them to be most helpful. Got my invoice the same day as the call to CA.