The simple answer is to go and buy a GoPro or similar. You need to reduce the weight to an absolute minimum, and whilst you could spend hundreds of dollars on different mounts, you're never going to fight the laws of physics.
That is using VERY stiff track-biased suspension, with solid engine mounts so the car rattles and shakes like a biatch. The camera was mounted directly the to harness bar, which is in turn attached straight to the chassis. No wobble or shake at all. It'll do 1080p @60fps all day long, and most professionals are now using these for their work (Harris and the DRIVE team, Evo et al) so they're definitely good enough. No zoom, granted, but you can change the angle from wide to medium to narrow, which helps. You cannot really zoom whilst on the move any way, so how important is that? You can connect it up to the 12v supply so will run 24/7, or you add a couple of bigger batteries. No biggie.
Bite the bullet, and make the change.