Readers have been very helpful. There's a whole world of call blockers out there. I am now investigating.
As a starting point, the video wiki ezvid.com has a Top 6 list and some explanatory material here.
Based on reader emails, common problems seem to be:
(1) These things are expensive. The range is $50 to $200, median north of $100.
(2) You're still stuck with managing a blacklist (i.e. "block these numbers"), although most models spare you the trouble of keying in the full number to be blacklisted. You just press a button and the last input call number gets blacklisted. So far, though, I haven't found a whitelist ("block all numbers except these") gizmo, which is what I really want.