Let me start by saying that plumbers are not appliance repairmen. There may be some experience with appliances, but for the most part, that's the desmaine of appliance repairs.
That said, I would guess that the problem may be a loose or worn belt. Unless you're seeing water laying in the bottom of the drum, it's the speed of the spin that extracts water from the clothing. Maytags were notorious for this, and required a kit to replace the belt and spring.