The new shower valve is probably what is called a pressure balance valve...it adjusts the balance of the hot-to-cold water if the pressure drops. Well, you have a major drop if you turn the supply to the WH off! It is just doing its job.
Does the pinging sound more like a tick or a ringing? My guess is that it is probably a tick. This is caused by the pvc drain pipe expanding and contracting while rubbing against something. So, it is all probably normal.
To get rid of the tick, if it isn't something else, you'd have to investigate the drain lines, identify where it is rubbing on something, and fix it. It is likely caused by a hole too small, lack of clamps, or rubbing against something.