So I called and tried to do the same thing I'd done before. I asked the cable company to dump my TV cable and keep the cable broadband account. It didn't work; my cable company is now subsiding my TV subscription. Apparently, they are desperate to keep the eyeballs on their screens.
Here's how it works out. Broadband alone costs $57 per month. Broadband costs just $45 if you are also a cable TV subscriber. The lowest, lamest, most limited cable package available is $10 a month. Ergo, it is $2/month cheaper for me to have broadband plus TV than it is for me to just have broadband. Very weird, but there it is; it's a better deal for me NOT to cut the cable.