You've determined that the pump is working as it should, and you are correct that this model will drastically slow down in spin if the tub is off-balance. Since there is no off-balance switch in here, the engineers made the transmission to slow down if the tub gets to swinging around too hard.
A couple of things can cause this....loose tub springs, worn snubber pads under tranny, etc. If the customer has had a habit of turning the water level too low, this will enhance the damage to the springs and such by almost always causing an off-balance condition.