I tried, but they started playing hardball, saying that if I didn't take the car from them (which they wouldn't allow me to do without signing a contract saying that I accept it "as is" and promise not to follow up) they would start accruing charges for storing it. I had just moved into the area for a job starting simultaneously, so unfortunately I didn't have the free time or resources to maneuver against them (The closest thing I got to legal advice amounted to, verbatim, "They have you over a barrel"). The whole situation seemed really sketchy.

Would reporting them for theft work? Tell them they have X time to give you your car back or you will report them for theft.