1) A list of cars that can be hacked up is available at the TLC website. The only two types of cars that aren't hybrids are the Crown Victoria and the Handicapped Accessible Minivans. Considering that you do not want to be 'on call' and pay 20k more for a crappy car, the answer is that basically NO minivans right now are good to hack up.
2) Besides, you can only hack-up new (<500 mile) cars, except in very limited circumstances, which involve medallion switching. So even if you could hack up an Odyssey, you probably could not hack up your own private car.
Good Luck, keep thinking of ways to beat the system.
Antoiln