Maybe this would work. Remove the stone halves from the base. Rotate each half 180 degrees and bring the square ends together. You should have two square ends that match up and the original bottom surface of the stone should be facing down.

Then glue what used to be the original top surface of the stone to the original [or new] base. When the glue is dry, lap the new top surface of the stone. I glue stones to wood bases using exterior grade liquid nail.