If access isn't an issue you could just bulkhead in the two supporting joists by adding layers of plywood to each side of the two joists. Add 3-4 layers each side, glue and screw and stagger the seams to span the 15 foot length. Just make sure the ends are properly supported on the concrete wall.
With the floor properly supported, you could build a stand that distributes the weight properly and if you add a layer of high density foam between the floor and the stand you shouldn't break any tiles. Grout lines might crack but that's easy fix, plus given it's marble or stone you probably wouldn't notice anyway.
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