Nigthmare on Easy Street ~
I tried to warn you without scaring you, but the experience I had with that Frankensteinian monster pump makes me tweak even now, thinking about it ;'>
They were so difficult to work on, an old repairman told me that they always installed a new pump, rather than open one up. Your pics are great. Ah, the memories and so wonderful for members to see how unusual the Easy pump is. In Reply 20 you see that rubber "hinge" that attaches to the flap? There is a tiny steel axle, or hinge bolt in there, and that's what I replaced because I like to close the drain on the spin side when an occasional load calls for a bit of softener; also if you use the flush rinse option instead of the needle spray, you need the flap, etc. My theory is that the rinse flap ages more quickly because of the constant water flow, while the wash flap passes water only a few times for a couple minutes per wash day.
Maybe you could pour/soak a solvent into the wash port or boiling water to free up the other flap, since like me you'll never open an Easy pump again.