If you heat the dop with a BBQ lighter, the stone can be pulled off by hand. Steeping both stone and dop in acetone will soften the glue and it will peel off without risking damaging the stone.
When I was talking about Blu Tack before I didn’t mean putting any on the dop to be glued to the stone. I meant holding the stone with it on the other dop in the transfer jig, so the preform is sandwiched between the two dops. It can then be accurately aligned, the dop slid back slightly to get some glue between the dop and stone, slid back in place and glued up.