I don't know that painting the back of the marquee will help. It could potentially diffuse the light a bit which might lessen the ability to notice the differences. It would be easy to test by putting some sheets of white paper behind the marquee and see if knocking down the light level helps in any way. If it works, then you will know if painting it will help. That said though, painting it could have a similar effect in blocking more or less light here and there. You might just try putting a white sheet of material behind the whole thing for consistency.
Not that it will help now, but for future reference, you may want to try using a "rich black" which is a combination of all the colors + black. That's the way actual printed documents get the deepest, darkest black. Typical is 100% black, 50% Magenta, 50% Cyan, 50% Yellow. Warm Rich Black would be something like 100%K, 65%M, 65%Y, 35%C. Cool black 100%K, 70%C, 35%M, 35%Y. Laser printed stuff can probably just be 100% of each (Registration Black). If you ask the printer, they might have a suggested % for rich black based on their printing ink & paper combination. I don't know what process they use in the marquee prints, so I can't be more specific. When I did reverse printed coffee packaging, we always were very specific about using rich black, as well as when we did higher-quality prints (with higher costs & better paper involved)