After my previous car rigging, I picked up a few suction cups to try a hood mount. These are just cheap double-cup models with a hole drilled through the plastic handle to attach the same piece of fence pipe. A weight on the other end provides some damping and prevents the camera from pivoting into the ground if the suction fails.
The big improvement this time came from finding a smooth, level parking lot where I could just push the car without the engine on. This made a huge difference in image quality. I tried a few off-camera and on-camera lighting solutions, but was really losing daylight too fast once the sun set.
It also turns out pushing your car around an empty parking lot while popping off strobes is sufficiently odd to attract the police. I explained the rig and the lighting; then when I explained that I was doing this for fun, he said, "well, that's a first" and bid me farewell!