Re: greenstone mouthpiece?
I've not made a mouthpiece from stone, but I've done a fair amount of mouthpiece work. Is the consistency of the stone rather homogeneous? I think this is the most critical factor as to whether it can work or not.
If it is layered or composite in nature, you may have a difficult time achieving a smooth surface, or you may need to apply a thin layer of epoxy to some parts of the inside to smooth out small pits and holes - particularly near the tip. Also, you have to consider the thickness and strength of the rails and chamber walls. Material that is strong when solid isn't necessarily strong once it's been hollowed out. All it will take is a vein of weak material in the rock and the mouthpiece could collapse under ligature pressure or stress while being played.
"The guy was playing low Bb so loud his mouthpiece exploded..."
I admire your taking on the challenge, though I recommend you monkey with some practice pieces before you take on this formidable project.