What are the statutes in your state, regarding estimates vs. actual charges?
If a shop is held–by law–to their estimate, or if they are only allowed to exceed it by a specified percentage, that detail could be used in your favor.
So, the first thing that I would do is to research your state’s statutes.
Perhaps a phone call to the Office of Consumer Affairs would yield the correct information for you.
The second thing that I would do is to resolve to never again go to Cottman, AAMCO, Lee Myles, Mr. Transmission, or any other chain-run operation for auto repair. These chains invariably are more expensive than independent transmission shops, are known for “bait & switch” pricing, and frequently deliver poor workmanship. Some people are suckered-in by their “nationwide” warranties, but those warranties have so many weasel clauses in them that they frequently deny any responsibility for subsequent breakdowns.