Can't fly out while you have a vehicle in Mexico?? True?

Yes you could do that by applying for temporary residence in the country where you live and then completing the process in Mexico, you would then be allowed to come and go at will but you need to have a Mexican address. You could then have your vehicle permit extended to the time of your residency. But you would probably need to first take the vehicle out and back in with a new TIP. I have had to do this. But not quite as to your situation.