I would guess you need to 'tilt' the cars in MED, as the real cars look to be "shaped" with that tilt.
And getting the rotation to be affected by the off-center mass, cant you just position the mass away
from the center of the car model?
Probably toward the 'high' point of the car, so it is a bit more reactive and "swingy".
(remember I am next to useless with physics)
I tried to tilt them within MED and I have a block behind the car so it does swing, but I can't get it to rotate the way like the real ones do, and I find it hard to explain what it does right now .. hmm, maybe I should upload a video

EDIT: Problem is fixed, just need the cars to rotate like on the pictures, originally 5 degrees tilt ><
I can get them to rotate properly, but that's only by rotating them with 'phent_addtorquelocal' and with 0 mass, but then I won't be able to get it realistic.
So all I need is getting the cars to rotate like that, and be able to let them accelerate by gravity AND mass, otherwise I won't get it anywhere near realistic! ^