I switched hosts, and when moving the database I simply exported the old tables via phpmyadmin, and imported them into the new host.
People can now post comments just fine, and they are available in the wp-admin "Comments" tab, however none of these "new" comments in the new host have shown up in my Recent Comments output.
The plugin has been configured, returned to default, re-installed, etc., but it still keeps showing the same old list of comments, regardless of how many new ones are posted.