In the end, the problem turned out to be some advice for completion-file-table-name I picked up from Stack Exchange: https://emacs.stackexchange.com/a/45246/13004

to ignore dot files unless they are explicitly asked for in file-find.

I don't propose to try to delve into it; most likely, the bug is in that code, and the reason that everything worked on one machine and not another has to do with different disk contents.

Many thanks again for your help.