Well, I HAD been intending to finally get the bathroom wall patched (where the last plumbing problem, in the shower, was attacked from behind, and still has a gaping hole next to the toilet), as my project for the weekend, but the kitchen sink had other plans. The steady drip decided it was time to turn into a steady stream.
Now, I don't know what codes or lines of thought were in place when the house was built in the 1930's, but let me tell you, if and when I get any kitchen remodeling done, my first priority will be PUTTING SHUTOFF VALVES UNDER THE KITCHEN SINK. Because the only way you can cut off the water now is to turn off the house water. This is NOT an optimal solution.
But it's sure motivation to get things done. Let's suffice it to say that I actually got the damned thing fixed, and I'm sure this was all caused by rasty San Jose water, which causes honking big crystals to form in the valves (!!!). (I'm really glad my cooking/drinking water goes through the Brita jug.) I still go visit the sink with a certain paranoia, like I just can't believe it has actually stopped dripping entirely. Maybe it's just I don't entirely trust my home repair skills? But it seems to be fixed for now, until the next round of plumbing woes.
Become a plumber. Be set with a job for life.