Sometimes it's time to replace an old shower faucet and go with a new pressure balanced faucet.
Moen makes the Posi-Temp, which holds the temperature within 3 degrees. Pretty nice if you have someone in the home opening faucetsa and using plumbing fixtures. It's also a good idea to keep current so that you will be able to get repair parts in the futures.

Your old valve may look like this. This was a bit odd. It came with a galvanized riser for the shower head.

I like to solder outside, making sure I get heat all around the brass fitting. I also pull the cartridge while I'm at it, and reinstall afterwards.

I sprayed the walls down a bit. That will dry later.

The cartridge goes back in, hot on the left, and the valve gets spun so that the notch in down.

And then the trim plate is reinstalled, to make sure that the tile is cut around this.