THANK YOU.
I finally worked through the ZipArchive topic — reloaded BPSP. Still error.
Never had any site caching. Theme is identical to other working site. Didn’t see a problem in Security Log that *I* could discern.
Disabled these plugins: bbPress Admin Bar Addition, bbPress Moderation, Genesis Toolbar Extras, Register IPs, TablePress, WP Edit. (TablePress is on other sites no problem. Bolded my guesses.)
NO ERRORS in 10 hours. Consider it solved.
Incredible hit numbers in S.L. blocks to an IP address for Request_Uris:
/admin/web_editor/
/system/htmledit/
/system/webedit/
/system/southidceditor/
etc.