Money talks, cash is LOUDER. If you're willing to hand over money on the spot a lot of people go well below their asking price, to have you drive off, or tow the car right off.
Also with a cash transaction, though it's not exactly legal, there is also no way to check how much money is changing hands, it's up to you and the seller, and means lower taxes.
Definitely get an estimate on everything that needs to be done to bring the car up to good shape, and use that to also drive the price down. I'd go with a solid on the spot offer of $4000 (depending on the repair estimate) and see what the seller says.
(If you think that's a low ball offer, last time I sold my even older crown vic, I was asking for $1400 and got offers of $400, sight unseen.)