Tony- I wouldn't worry about cutting the green marble.
You can even work around the green and leave it polished. It would be a nice contrast with the main floor being honed.
We do a lot of floors like that-designers love that stuff-
I don't know the size of the floor or the name of this stone. Sometimes(probably a hard marble) it can be hard to break a polish on a surface.
I would recommend that you use 3 inch electroplated diamonds, Hybrid copper diamonds or 120 coppers to break the polish. (or a combination of those)
The 120 bulgarian electroplated pads that we sell will give you a nice clean scratch pattern that can be followed by a 220 copper hybrid then back to resins or even poly pro or vortex.
Did you try a vortex black dot ? Also I would speak to the client about possibly flattening this floor.