Water comes out of the shower head when faucet is in tub fill mode (I know why, but not how to fix)
Most likely the problem is just the diverter on your tub spout, it's probably not opening all the way, which allows some back pressure to build up in the pipe that eventually gets back up to the shower head. It could also be corrosion inside of the pipe that is having the same effect. 

I don't see how it would have anything to do with the height of the valve, unless maybe the lack of head pressure (weight of the column of water in the pipe) isn't enough to overcome the back pressure created by your diverter valve. The Moen valve is just on or off, it doesn't tell the water which way to go, that's done with the diverter.

If that doesn't do it, the other option would be to put a shut-off valve at the shower head spout. Same net effect, no need to open the wall.