This quest is very easy if you know what to do. Don't bother driving around the map looking for a nice steep hill or cliff to drive off. Build yourself a ramp and drive your car off the end. The ramp doesn't have to be super long, 5 or 6 tiles will do.

If you come across some Chonkers off-road tire you can thrown them on the car as well. They are not required of for this quest but do make it easier.