I know, that sounds weird. But I just returned from the dump/recycling center, in my case the one on Omohundro Drive. I dropped off the old dishwasher along with my usual recycling and household trash.
Anyway, the woman there told me that today (Saturday, May 15) is an unadvertised “amnesty day” when you can drop off ANYTHING (other than nuclear waste, probably), and you can spread it out over three trips. But hurry, I think the centers close at 4 or 4:30.