NM, we finally decided the only explanation for the problem must be some form of SQL database corruption. So we searched for available methods to repair the database and discovered WP-DBManager plugin (https://www.ads-software.com/plugins/wp-dbmanager/).
After backing up the SQL database and running the WP-DBManager database repair option the problem with the two subdirectory based WordPress websites appears to have been resolved. FYI for anyone else having this type of problem.
