Over $6000 to install TTI headers on 66 Barracuda

I would get it out of there. Working in the industry, I can tell you that you own the car, not him. He can't stop you from taking your car and not paying. (Though he will try) A shop's only recourse is to deliver the vehicle and try to recoup their expense through the courts. $6000 for a job that was quoted $1000 is excessive and he will lose in court.