Well, one thing; what is the resolution of the method of printing? because you may be 'over the top', a few folks I know of who do t-shirt designs often have the problem of submitted artwork of a higher dpi than their screens, for instance.
Sounds like you're probably past the resolution of Atari's own film-based screening methods of the time.
How I would approach this:
Build an illustrator file of the appropriate size, making a vector blue grid to scale. (easier typed than done, I know)
From looking at the referenced backglass.jpg file (which even that makes my computer hiccup)
it looks like the background colors are solid (dark blue inside the grid, black outside)
and what you would want to isolate would be each element unique to the source;
The 'Star' would need to be printed as-is, but the 'Wars' is a solid color.
for example. You'd have a vector white and a vector black placed in layers above the original gradient art for the letters.
The X-wing, and Tie fighters would also need to be used as-is. Same with the stars.
The death star is the only one that's really integrated into the grid, even the stars have been illustrated to fit within the blue grid rather than overlapping (note all the 'half-stars' throughout the design to account for registration errors in printing.)
Hope I haven't confused the issue further. .
But that's how I took nic6paul's image (thanks!) and made my own upright marquee; Almost there.. still have some grids to fix.
I can see how you have a problem with the file sizes; mine adds up to 150 megs. But that's photoshop pixels, not illustrator.
I would _not_ want to take on the whole big backglass unless I had a machine to put it on..
Somebody lend me theirs so I can.. um.. test the fitting. Yeah, that's it..