I use a band saw most of the time. I have used my diamond tub saw, it does help with the elimination of the dust. With a vac at the blade port on the band saw, and the saw running at slow speed, a band saw works fine. I suppose there are doublets of MOP out there (to make thicker pieces?), but all the material I have ever worked with is solid. The shell is cut so there is a show side and a back side. The back side can look very plain, and the line of demarcation between the two may look like a lamination, but it is a solid piece. If a doublet was made in MOP, it would be a good quality MOP top on a common shell back, but surely nothing that is real MOP would have a glass or quartz cap on it.Some of the composite MOP scales look like they have an acylic top?
I'll try to look in the shop when I get a chance, and pull out a box of red abalone shells I used to cut slabs from, for some photos.
As for grinding it, sand with slow belt speed, avoiding heat buildup. A wet sander will be a real advantage if you have one. Sand to 400+ and then buff with white rouge,again avoiding heat build-up.Wear proper filtration gear, vacuum up all dust, blow the dust off your clothes outside before going in. The dust form many types of MOP is not good for you at all,especially abalone.
Stacy