OK, I have a happy ending to report, here is what happened.
When my old computer died (catastrophically, with no recovery possible) I bought a new one and restored everything from a Time Machine backup. What I learned from a helpful Adobe tech support rep is that license info among other attributes is not saved in a backup. The solution is to "sign out" of the old copy then reactivate a new copy. Except this is impossible if you don't have access to the old machine to deactivate. Trust me, it doesn't work going to your Adobe account from a different machine! Eventually the rep found a back end way to deactivate my account manually, which then gave me the ability to reinstall and reactivate with my original licence code.
So for those who think that "no one should fear getting cut off from LR", good on ya, cultivate some helpful tech reps. Also, advising that all would be good had you managed your library differently for the last 10 years, is seriously unhelpful. I am a lowly amateur who didn't even know about such exotica as XMP sidecars and had no ability to create them after losing access. That is just not useful advice.
I know better now, and will be exporting JPEGs of all final images. I will also be actively seeking alternatives