Go check out the 'boneyard' of your local granite/quartz/marble countertop fabricator. They'll have all kind of options for very little. It's only when they cut and finish the edges does it get spendy. I like quartz because it's a mineral filled resin that is very dense (25 lbs/ft2) for the 3cm and very well damped because of the resin + mineral composition.
Guitars are different - you want them to resonate, but in a very controlled way, that's why the bodies are thin wood, usually very stiff, but no one would ever confuse rosewood with mahogany or maple used in the backs or sides. Spruce of varying species is preferred for the tops, with mahogany and maple used for specialty instruments, like a 'Hogtop blues guitar, or a Gibson Maple Jumbo with a midrange voiced to cut through the rest of the band. A neither sounds anything like a Martin Dreadnought.
But I don't think most people want to use vibration platforms as tone controls, so dense and non-resonant is the better way to go.
