How do I secure the shower valve without removing tile?
You'll have to be creative, but the best solution is to open the wall on the opposite side behind the valve.  Hopefully you have drywall or a closet and not an outside wall.  Drywall repair is cheaper and easier than tile repair.  In many areas it is code to have an access hatch to reach the bathtub trap, so you may be able to reach it from there.

Other option is to bust out as few tiles as possible.  You should have a few spares from the tile work, or if it is recent you may be able to buy a few to patch the damage.