Yes, yes, crazy question

[robobass]

I bet acrylic (Plexiglass) wouldn't sound so bad. It is not soft at all. There is cast and extruded acrylic. The cast stuff is actually rather brittle. You would need to use to use fairly thin sheet ~3/16 -1/4" so it would have decent acoustical properties. Unfortunately, it would be quite fragile. I worked a lot with acrylic in the '90s. I mostly used methylene chloride as a solvent. Acetic Acid is stronger, but can yellow. Sounds like a fun project if you've got a buddy with a big vacuum thermoforming facility!
Robobass

[Yvarg]

I know no one who has any vacuum forming equipment. I usually buy an oversized piece when I'm make something from the stuff and carve out whatever I want to the right shape, sand with a number of grits working up to about 600, then lightly melt the entire surface of the piece with a propane torch to fill in the scratches and restore it to the original state of transparency. I have no clue whether that affects the structural integrity of the piece or not, but I've had good results so far.

[Turnaround]

Twenty-odd years ago there was a company that manufactured really high-end turntables from plexiglas because it was non-resonant. Perhaps it's not a good choice for an acoustic instrument.

Then again, if it's visuals you're after...