I'm trying to avoid this by printing the parts on a prepainted black card sheet.
Moshe, how about pre-painting the paper grey instead of black?
Then you could print the outlines in black (or some other dark color). It might even look more realistic - tires are often some kind of charcoal grey, especially if they are older and sun-bleached (example below).
Eager to see your M35, it's such a handsome truck. Good luck!