Over $6000 to install TTI headers on 66 Barracuda

You verbally discussed paying him $1000.00
I would not pay a cent more...even though that's 2X what it's worth.
If he will not finish the job for that amount, hire a tow truck to go get your vehicle and flatbed it somewhere else for completion.
6k is ludicrous and not even anywhere near sane.
Sounds like he's trying to make up for a bad week. His problem, not yours.
Contact the BBB once you have your car.