Hmm.... disabled the plugin called 'better-wp-security' by renaming its directory since it's got plenty of features that could break a site... a hail-Mary attempt to fix things... and the site works again.
However, I haven't had an upgrade offered for that plug-in for a while and haven't made any configuration changes.... so not sure why things have suddenly broken...
For that matter, I don't think I did any updates before the site broke. Is there a way to see a history of plug-in updates etc.? Something is screwy...
The BuddyPress site that has worked throughout this issue also has better-wp-security installed and running, along with essentially the same group of plug-ins... which also makes me want to dig deeper.