Macmikeman:stated,
"I will cut off the bare ground conductor at each end right at the spot where the sheath is opened up to. That way I am using two hots, and an "insulated" neutral conductor. I wonder if others will see fault with this method?."
I believe section 250.4 might apply. Noncurrent carrying conductive materials enclosing...etc.
Unless the outer conductors are bonded to something a break in the inner wires could energize them (the outer) and create a shock hazard. If it were a metal conduit enclosing conductors you would never leave it unbonded.
Alan -Inspector