I think I would use a Accelorometer shaker table, then mount multiple accelomometers over the billet. This should give you a nice map of the actual variations of each area of the billet (MDF) in question. From there you could then take pieces of the same size with the grain running in different directions, and different densities, and see the variation from the original. This would give you the ability to predict with atleast some consistancy of how the resonant frequecies will come out.
This in turn would give you the ability to try to find the perfect wood grains to get the "tone" you are looking for from any guitar you are building in theory anyway.
As for how to suspend your billet, from the primary labs that I i have seen, I would suspend your piece from 4 corners (this will keep any outside noise from effecting you readings) and place a speaker directly below the billet and use a swept sinewave, one again you'll have to use multiple points to get a good mapping of your billet.
Once again this is just my .02 I am not a physics major and I never played one on TV.