After more work than you'd expect (given where I was yesterday), we have a functioning sink, dishwasher, and yea, even disposal. After a trip to Home Depot, I discovered that my original dry-fit plan wasn't going to work (even if I'd gotten that last piece in the vent stack), so I made another trip to Home Depot for more fittings. The trip was totally worth it, though, because I saw this in the parking lot. Apparently it was the last day for someone named K.C., and his or her co-workers bid them a fond farewell by wrapping their truck (with a Home Depot shopping cart thrown in for good measure) in plastic. The antenna has a cardboard tube with goodbyes written on it, so K.C. will know who to blame.
So I tried the ultimate test -- starting the dishwasher. With little fanfare but much excitement, I let it run a 'quick wash' cycle, and all was well. Woohoo!