i was thinking of doing the same thing awhile back, the plexiglass idea doesnt work well because of the translucent thing you were talking about, but higher grits of sandpaper might work to get back to that clear look, like 1000 grit or something you can get at a car body shop....
also i had the idea of making a molding of the guitar shape i want, then getting some clear liquid that hardens like wood or something at an art store (cant remember the name of it but it was a resin or something that dried clear) and pouring that into the molding. For the pickup cavities you could put a block of wood so the liquid goes around it, but........thats a hell of a lotta work.
lastly thick sheets of plexiglass are super expensive...for me atleast, i called american plastics and they told me for a 20 x 16 x 1 3/4 (inches) was about 200 dollars...
sorry to be the bearer of bad news man