Thanks wbrian63.
The cup holder in the pics was made using solid wood. I didn't veneer both sides because I thought the wood was thick enough with small enough dimensions to avoid any problems. I also coated the whole piece with Helmsman Spar Urethane in addition to the multiple layers on the veneer. The wood has the grain running perpendicular to the grain in the veneer too.
Achieving the smooth surface was easy but time consuming due to applying the urethane, waiting for it to cure, sanding it smooth, wiping it down and repeating until it closely matched the appearance of the wood in the car.
I believe I'm going to make all the future cup holders from MDF which will be completely varnished to seal it ... I already thought of spills, as my wife has spilled her coffee in every vehicle she's owned so far.
I'm also going test to see if Goldspar will be a better choice for the finish as far as building up layers faster.