Since I had to redo it all anyway, and we already had the new valve body, I just went ahead and installed it. I'm sure a good plumber wouldn't have taken as long as me (4 1/2 hours!) but in the end it all works (no leaks and hot is hot and cold is cold) and I'm pretty proud of myself. I took my time and was careful.
That was actually all done last weekend.
Today I added the last of the Hardiebacker in the shower area. This time instead of scoring the board with a knife and having a hell of a time getting it to snap cleanly, I put the concrete blade on the circular saw. Man the dust that kicked up! It was raining so I did it in the garage. Probably not the best idea. I had to wash both cars afterwards!
While I had the saw out and setup I also cut the Hardiebacker for the fireplace. It really helps define how it'll look later. I'm also really happy with the height.