It sounds as if there is a clog at the Moen valve.
I would consider removing the cartridge and seeing if that needs cleaning or replacement for starters.
I am having a water pressure problem in my master bathtub. I turn the water on and for about 15 seconds I have good pressure, but then the pressure drops. The facet is a single handle Moen. It doesn't matter where the handle is (on hot, cold or in the middle). It takes about 7 seconds to fill a 32oz bottle. My other bath takes 4 seconds. If I fill the bottle right when I turn it on and the pressure is good, it takes about 4 seconds. What could be causing this pressure drop? The house is less than 2 years old.