Why it's moving-- is the fact that when you "tapped" the shaft into its final location the center of the pto hub on the flywheel was forced off center. When the engine is cranked the effect internally is like a camshaft lobe and is causing your hydraul-shift to move around.
A quick check to see if the above is true is to yank the pto shaft and crank the motor. If there is some scuffing on the shaft, there is no need to turn the motor.
Before you inserted the shaft you should have had the sprockets parallel and on center. The manual shows how to do the proper alignment with various shim thicknesses.
What I do is insert the pto shaft into the 3 speed before I drop the motor in. Just to make sure murphy isn't lurking. Good luck.