If the plexiglass is a PERFECT fit, then you can tape off the areas that aren't big enough and spray paint black the tiny light-leaks.
Or, here's an idea I just thought of, Go to home depot and get the foam wetherstripping, and put it on the back of the back piece of plexiglass. Stick it on so it goes too far out to the sides, so when you install the marquee, it squishes the foam, making a perfect fit