Vinyl on the inside could look fine - I'm just thinking you'll have all the tactile qualities of vinyl.
Could look more upscale to make some panels that wrap around the outside of your plexi walls and install the vinyl on that, so it looks like carbon fiber behind glass.
Or I was thinking of something like making those outer panels also of plexi, frosting it with a random orbit sander on the "inside", using carefully aligned horizontal bands of clear double sided tape to bond it the outside of your existing walls, then edge-lighting that, or maybe your existing lighting is good enough to make a complimentary glow right up the frosted panels in a cool ethereal way (fade). There's even a chance that the tape edges might make some cool lines around the sides.
Either way, with all that plexi I think keeping the glass based aesthetic would keep things more in-theme, but of course take that with a grain of salt -
I'm not there, I can't see it in person, and this is your project not mine.
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