So, what you do, is you print all your marquees on a continuous sheet of flexible transparent plastic, and you motorize a scroll like old metro busses used for their "Destination" sign.
Your frontend tells the arduino to bump the motor to reel, say, 14 marquees worth of vertical feed off the top reel onto the bottom reel, and what's exposed in the middle between the rollers in front of your backlight is the current game.
You can have a couple idler wheels up front to match the traditional arcade cabinet profile, the big takeup reels can be buried back in the guts of the machine.