Ha!! The first crazy idea that popped in my head was a pair of Jumo 004's from, say, an ME 262.
Jets would be wild to see but since you are going for off-the-wall on this build, you could cram an aircraft motor under the hood and build a folding prop.
The trick with the original car was that there was no outward indication that it could fly. It wasn't until everything had popped into place that you knew what was special about the car.
I can't wait to see what you come up with. What a great idea... an up-date on an old classic.
Matt