Resolution

... bit of a denoument, really. They ended up sending the dishwasher part to my parents' house via an employee who lived in the same neighbourhood. Which was very nice of them. I can imagine the conversation they must have had...

Manager: uh, so what's going on with this dishwasher thing?
Staff: Oh. My. God. you wouldn't BELIEVE this woman, she keeps calling and calling. Can we just send her the *@!!$# part?
Manager: yeah, I guess, just don't kill yourself doing it. Doesn't Bob live over thataway? maybe he can take it.
Staff: WHAT.ever! just get her off my back!
Manager: alright, don't have a bird. Bob can take it.

And the next day, Bob (or actually, Bob-ette, it was a woman) shows up with the part. Voila! Luckily I happened to be at my parents at the time, and I was duly grateful. I gave Bob-ette the original dented part, just to prove my point. She took it, though I heard her thinking "what does she think I'm going to DO with this?!? I don't even work in that department!"