Here is a suggested battle plan....
Before you start your battle, get the owners name and google it. Find out where he's lived. Visit the state department of corporations and find companies that he has registered, both dead and alive. Search courthouse databases for him and his businesses. Visit BBB and see if there are any complaints. All this should be online. Dig up some dirt. And with note lot owners...you will find plenty.
Then call the dealer up and ask for the owner. Tell him you are going to return the car and for him to have your money ready. ALL OF IT. You do not want the car fixed. No deals.
If and when he refuses, get angry. Raise your voice a few decibels and deepen it. Tell him that you are going to be a major, MAJOR, fucking heat case. Click off the names of people that have sued him, and promise him that you're going to be much tougher. Tell him about your good friend at a local media outlet....and that you're going to find the most pain-in-the-ass lawyer working on the case. If you found any court cases that he lost, find the opposing attorney's name and drop it on him.
You want to do a full scale attack early. Most of these note lot dealers sell to uneducated people working two or three jobs, and too busy to fight him. But if he sees you as a Bit Pull with oodles of time on your hands, he's going to make a fast decision to surrender.
Just for future reference...the objective of a note lot is to eventually repo. your car. Buy here pay here lots sell junk. Never buy from them, nor buy a recondition title car. Ever.