Hi, JW - Thanks for the reply!
I have actually had the dishwasher all to bits, and examined the flap in question. It's pretty much solid.
What I have noticed is that there seems to be inadequate output pressure from the pump. If I hold the drain hose down near floor level when the washer is draining, the water comes out in a pretty full stream. If I lift it up to sink level, the stream reduces down to a trickle.
Would that be a problem with the pump, or the motor. Or something else?
(Oh, also the coupler between the filter and the base spray arm is completely destroyed. But I doubt that that has anything to do with draining. Does it?)
Thanks for helping me think this through!