The new tile floor in my kitchen with 14 inch tiles are clicking. We pulled
up a few and reset with more mortar but more are clicking and I think a few
of the originals.

I am afraid the subfloor (two 5/8" plywood sheets) moves too much. It has
been suggested that I pull up the bad tiles and then screw the floor to the
joists. Will this be sufficient? The floor does seem to move when my 250
lbs walks on it - the movement can not be seen from the basement - it is not
the joists. Would additional cross bracing installed from below help?
Would additional wood from below then screw up and pull down work (plywood
does not hold screws well. I do have full access from below.