Perhaps you could take a trick from films? When you are "driving" all you really perceive is the "interior" of the cab (the dashboard and instruments) and the view through the windows. That is in effect your "set". Any other view of the vehicle is an "exterior", which is a different "set". I thought this was where Mktavish was going with his idea of two "creatures". You just switch between sets (perspectives) as needed.
If you have a functional approach with the "flea" cab, then the only difference with a larger vehicle view from the cab interior would be the vehicle hood/bonnet. Everything else would be an "exterior" view, with the possible exception of the view out the rear window or mirror. But that view of the hood/bonnet would still remain basically the same. It's what's beyond the bonnet that would "rise up" or "drop away".
I suspect part of your problem is that you are just letting the havok physics take over, which IMHO is a mistake. When you drive a vehicle off-road or up/down grades you don't let the vehicle throw you around any which-way, nor do you try particularly to remain in the same vertical axis. You try to retain control which includes maintaining a clear view through the windshield of your route. When climbing you don't tilt forward; you push yourself back in the seat by pushing on the steering wheel with your arms (or are restrained there by a harness) so you retain a "straight ahead" view of the "road", even if the view is tilted compared to the horizon. The same is true when you are descending a hill. Your focus is on remaining on the "road", not on the horizon.
Even when you are thrown from side to side, you are actively moving your body (or at least your head) to remain "upright" to keep that view, which is why you lean/tilt in the opposite direction. From the perspective of the cab interior your goal is to maintain the axis of view through the windscreen to the road, not through the vertical axis of the "driver". The only time you might lean forward is when you need to check the clearance between the cab roof and any overhead obstructions.
This is not something the havok physics system takes into consideration as far as I know. So you may have to devise your own mechanism if restraining the body against the seat is not sufficient.
Just another perspective on an interesting problem.