Another option would be to have an extension fabricated and threaded for you in the correct length.

To Dragonfly's point. Notice the tile frame around the square shower heads. A tile profile can be introduced and the center built out as needed.

Drill out a couple marble circles with a hole saw. A 3" and 4" perhaps. Adhere them together and finish the edges.

Would it be easier to cut through drywall on the back of the wall and properly correct the plumbing?

Thank you for the brilliant ideas! We may be able to access the plumbing "oops" through the back of a closet. Otherwise we might try to fabricate an adaptive piece. But to whom do I turn to do such a thing?

"But to whom do I turn to do such a thing?"

Let your plumber figure that out if the error is his.

Unfortunately, my plumber suggested getting a different handheld unit!! I carefully selected the multiple - piece shower system, and refused to do as asked. He suggested I "figure it out", since the "tile guys applied the tile too thick". So after talking to a Big Box store plumber I decided Houzz might help me solve my problem. Thank you.

Maybe contact the manufacturer to see if they have adapters that might work?

You will look at the valve fix daily. You will look at the back wall of your closet when?

I wish all my decisions were this difficult:)

not all plumbers and tilers understand FWT which needs be communicated at rough in stage, also alotting for out of plumb walls. Finished wall thickness.