Lots of the good words here. Go in person. Try to make an appointment, or at least leave a message that you will be there about X time and want to talk to the decision maker, and call back if that time is not convenient. Keep smiling. Never get mad. Mad words are like throwing sand in the motor. They just jam up the works. Smile a LOT. If you have to buy the parts, it shouldn't be more than around $700. Offer to pay $4-500 if he pays the rest of the parts and the R&R and rebuild labor.

A good deal is one in which both parties are equally dissatisfied....

Your final alternative if the in-person nice bit doesn't work is small claims court, or perhaps your state has something like my state's Governor's Office of Consumer Protection or a similar auto repair watchdog. Mostly toothless, but often inspirational to a balky shop manager. Getting served with papers from small claims court is nice, too, and may motivate a return call.

Small claims is informal and common sense. If it goes all wrong or you screw up somehow, you can get a "de novo" hearing in a higher court. De novo means a clean do over, no harm, no foul...