One other thing that you might try, since you plan to put them on the hook for the cost of repairs, rental/loaner, tow, etc.. etc.. Would be to present them with two options, and let them pick:
1) Dealer #1 pays to replace the engine with a quality new (or certified and warrantied used) long block, plus cover your rental for the entire time they have the car, plus reimburse you for the to expense, your costs with dealer #2, and any other related incidental charges, and then warranty the repair (engine, parts, & labor) for at least as long as the original factory warranty covered the car
or..
2) Replace the car with a new '16 or newer, with equivalent features.
Given the time, paperwork, and effort involved in fixing the 'old' car, they may simply choose to make things easier and give you a new one.