Purchasing a car from a private seller. Nightmare.

The OP is lucky that IL allows third party sales. You will no get away with that at Fl. DMV. I would never buy a car without an open tittle. That part is totally on the buyer.
Really? I've bought a bunch of cars, trucks and boats with a third party title. Never had a problem. People at the tag office never ask for a bill of sale or anything. The last one was a South Carolina title. Only thing they wanted was a vin verifIcation. LEO friend stopped by and filled it out. Silly since the dash was out of the car and I could have hauled that down there but I didn't mention that. Lol