So many angled surfaces, so many opportunities for reflections. How many are acceptable is somewhat dependent on the end use of the image. "Controlled" reflections can add to the aesthetics of the image, while "uncontrolled" can distract. You've done a good job controlling what you could under the circumstances. Most don't have a studio large enough to house a cyclorama wall, so about all you can do is embrace them in the image. I also like the staging for the shot, great location, adds to the drama.
Unless you have directional light, a polarizer isn't going to help much as the polarizing effect decreases, as the direction of the light moves away from perpendicular. I've used cross polarized lighting on small objects with good success, it would be difficult on a large object (not impossible).
The easiest (though not the most predictable) is to chose your ambient light time of day or weather conditions. Early morning/late evening seems to work better. Even better, a cloudy overcast day is like a giant softbox that bathes the car all over. Last year I had the opportunity to attend the "Mother's Route 66" car show in Springfield, IL. Middle of the day and heavy overcast, provided the ideal light, static subjects and no wind made Pixel Shift an option to pop the colors.
Illinois Route 66 Mother Road Festival as you'll note it didn't completely kill the reflections, but the ones remaining blended well with the environment.
Another option I've used is to create a composite with multiple shots blended post. With camera and aperture locked on tripod you can adjust exposure (shutter), use reflectors or strobe to work individual sections of the car.