So I finally got around to doing this mod. I bought a sheet of plastic brick at a model railroad store here in Denver (it was actually labeled as "concrete block" but I liked the size/texture better than the smaller "brick" sheets).
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I measured the area and trimmed a piece slightly oversized, then sprayed with Ace Red Oxide Primer. I let that dry for a few days, then hand brushed over it with a wash of roughly 10x water to 1x white acrylic paint to add a "mortar" look, mopping up the excess with a paper towel but leaving some white behind in the spaces between the bricks. After that dried a bit, I followed with a wash of 10x water to 1x black acrylic paint to add a touch of "grime" (I used cheap $1 flat acrylic paints from Hobby Lobby, but even gloss probably work OK given how diluted it is). If you wanted to match the brick plastics and the sanctum (which have black "lines" between the bricks) you could do the black wash alone, but I like how the white "mortar" makes the individual bricks stand out a bit more, and the white wash also gives the bricks a realistic faded/weathered look.
Here it is installed, I'm very pleased with how it came out, it has a three dimensional look that doesn't come out well in the photo but definitely beats a sticker from my view:
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It was actually more of a pain to install than I would have thought. I describe my approach below, but if someone who has done this has an easier/better method, hopefully they can post it!
The main difficulty was in figuring out where all of the screws should punch through the plastic, which is thick enough that you cannot "feel" for the hole as you might with a piece of paper or a sticker. After removing the three flasher domes (and the flasher bulbs and fixtures from the rear) plus the two screws holding the plastic ball trough to this section of the back panel, I trimmed down my brick sheet to final size. Then, starting on the lower left and working my way across, I would eyeball where I though the screw should go and use a safety pin to poke a hole through. If I guessed correctly, I would then expand the hole a bit with a scalpel, and then put that screw in and move on to the next. This took some time, and required expanding/adjusting some screw holes with the scalpel in the end to avoid unsightly flexing in the sheet of brick. When I had the screw holes where I wanted them, I poked the safety pin through the flasher openings in the back, and then expanded those three holes out to the appropriate size from the front using the scalpel.
Once I had the sheet of brick installed, I found that the plastic ball trough was pushed a bit further off the back panel and no longer aligned well with the upper section of the trough coming off of the battlefield. This was an easy fix -- I added a spacer to the right-most screw on the upper trough section and it now aligns perfectly (as you can see in the photo, what looks like a red ring behind the screw on the clear ball trough to the far left is actually a screw tab that I snapped off of a spare flasher dome, but an appropriately sized washer would work too).
A fun mod and one that makes the back right of the game look much, much better. Just reserve some time (and a few curses) to get the screw holes punched through!