I took a two-pronged approach -- first, I carefully masked off the tube and spray-painted the monitor frame a flat black. Worked out great.
Next, I mounted the monitor in the cab, put the plexi on, and marked where the visual edges of the screen were on the plexi with a magic marker. Then I took off the plexi, masked off the monitor area on the back of the plexi (and an area for an instruction card), and sprayed the _back_ of the plexi black. End result is, at least to me, a very professional looking final product.
Kevin