Ok - all done. It works great! That is, once I read the instructions and realized that the water has 2 settings - pump and rinse. At first it was filling up the tanks and couldn't figure out why. The rinse feature is awesome. I couldn't believe the, er, junk that came out of the black tank even after it was empty. I rinsed it and drained it about 5 times until it was clear. Ditto with the gray tank.
Not a drop spilled in the basement since I let it drain for about 30 minutes before I disconnected it. It's not elegant but it works. I may come up with a more permanent solution in the future, but this is great for now.
