The plumber finished up yesterday as promised. A miracle was performed under the sink!
Everything under the sink was replaced. I can now tell what everything is and where it goes, and I can easily shut off the water to any water using thing in the kitchen without fear of a great flood. This was more expensive than I had originally thought, but it's done and I can change easily change out the sink and faucet myself in the future if the need arises.
As an added bonus, I can now put the garbage and the recycling under the sink. Neither one used to fit, so this a huge win. It's like the plumber magically created extra-dimensional space under the sink.
I'm really happy with the sink and faucet, too. It looks so clean and fresh.