How about this Laythe:
I've been turning this over in my head today, and I think there may be a way to combine the two ideas, and use drawer rails with maybe a piece of 1/4" ply combined with fabric skirting around the screen flex points if needed to get the same effect. You're absolutely right, this wouldn't be bearing any kind of load.
So here's the idea -
With the way the cab is built, I needed some kind of better structural support for the middle 16 or so inches, since that's where all the drawer rails for the pedestal and screen movement live. So I built in shelves on the sides, to essentially help brace the main supports by attaching them to to the sides of the cabinet, but also to store lightguns / controllers / guitars for clone hero / extra joysticks and spare parts / etc.
I think this is one of the better shots to display the shelves:

Anyway, the thought is that I could add a set of drawer rails and panels on the wall of the shelves, or even on the side of the cabinet and attach them to the screen drawer, or even directly to the pedestal so that they slide out when the pedestal and screen do. And for any cutouts that might be needed to accommodate the screen tilting, I could use a scaled-down black fabric skirt for, so that it would flex with the panel, but still hopefully be neither too obviously visible, nor visually detract from the overall profile.
Something like this, maybe?

If the panel rails are slightly below the main screen rails, that may even let me attach this directly to the pedestal without interfering at all with the screen movement. I'll have to see if this all actually could fit together in a feasible manner when I get back down there, but even if it requires some tweaking, I think this may work.