The marquee for my game seems to not exist. How would I get a sheet of them printed on that heavy plastic?
Custom made would be the way to go. This user; stpcore (on arcadecontrols.com), makes custom marquees. Gameongrafix is another online vendor offering customized marquees.
I've seen on craigslist a few local places that print game marquees. They usually have a list but I bet if you find one and have a high resolution picture they'd do it for you.