Permanently Delete IMAP Account
The problem was an intractably corrupt iCloud keychain.  The cure:


Disable iCloud Keychain Security code approval on every device.
Disable iCloud Keychain on every device.
Use Keychain Access to reset a Mac's keychain to the empty default.
Re-enable iCloud Keychain and security code approval on every device.
Use Keychain Access to manually move desired items from the corrupt keychain into the new pristine one.