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One last thought if you don't want to do any of the above. You can also pay with a credit card, then file a chargeback with the card and state that you didn't authorize the work, the repair was done without your consent and was done poorly. Credit card companies definitely have a lot of power in these cases. The shop will have to show proof that you authorized the work and if they can't do that, you would likely win the case and get your money back.
Best advice.. OP says mechanic is well regarded and does not want to burn bridges. If it is not too much paying it might be best. Otherwise paying with a credit card gets you the car back and if you have a good case the credit card company will back you.
This law went into effect in Ohio in the 1970s. I was working at a Sears auto center, people would come in wanting the advertised 19 dollar muffler, then they would be shocked a few hours later with a bill for 60-100 bucks. Well it needed hangars, pipes, connectors, etc. After the law went into effect we had to lift the car, inspect, write an estimate, present it for their approval, at which point about 1/3 of them said Nope give me my car back. Manager went ballistic at all the time wasted and sales lost, but had to comply with the law.
Funny how some people are like that when they can no longer get away with fraud.