Hi Mike, you can reuse the old tiles but the thinset needs to be cleaned off the backs. A pair od tile nippers works well to nip off the old grout. A grinder with a 4 inch blade will cut off the thinset without a problem. The thinset also needs to come off the cement.
Most likely the movement within the crack is causing the tiles to come loose. I don't know if it will work but I might would try to leave the tiles unstuck in the back, on the small area on the other side of the crack. Just letting that small area float might keep the pressure off the tiles. Silicone that joint.
Maybe someone else has a better idea.