Creating an ingame LED Panel, with modifyable scrolling text

Basically, I'm trying to create one of these, in a standard FPS environment:

The player should be able to set his own message and the text should scroll from right to left repeatedly.

The basic concept is easy to do: I have my screen model, I put a 3D text mesh right in front of it. I make a script that can modify the text message from elsewhere.

The tricky part is creating the effect of the letters being scrolled over the screen. What would be a good way to approach this? I was thinking of animating the text to scroll from right to left in front of the screen, then reset it's position to the right again, repeat. Then I would need some kind of mask to hide the text when it's off the sides of the screen.

This solution could mean I'd need a shader that creates this mask. I'm new to shaders, so if this is the way to solve the issue, my question would be how should my shader work?

Or could there be a completely different approach to create a panel with moving text like this?

Thanks!