OK, well, the good news is that the washing machine drain hose popped off the back of the washing machine. Easy fix, IOW. The guy charged me only $110 for the weekend house call, used my shop vac to suck up some of the water in the carpet, helped me arrange some fans to start drying it out. He said his guess was that the water didn't go through the floor so much as underneath the access panel and that probably that's how it wound up in the basement. He also gave me advice about how to replace the hose, and how to test the new one before I put the washing machine back.
So on the good side, I had him give me his card so I could use them again. SUPER nice guy. I actually used that company when I moved in, to put the washer and dryer where they are now. At the time I thought they were a little pricy, and I've used several assorted plumbers since then and haven't been happy with any of them. So from now on I think I'll stick with these guys. They've been around for a long time and were recommended to me by the previous homeowners (you know, the lucky devils who sold this place JUST in the nick of time).
I've ordered my new hose and will go pick it up at Lowe's shortly. At least I know now what happened. It's that "oh f*ck, what now" feeling that is so disconcerting. I don't think the appliance repair company would have been a whole lot cheaper, and this has helped get it off my mind a bit.