I got it working again by deleting Joomla's cache. It could have been something else I did but it didn't go into effect until clearing Joomla's cache. However, on the ".au" site, I did nothing but clear Joomla's cache and it fixed the issue.

On just the ".com" site, I updated the plugin, modified the .htaccess file, changed to HTTP instead of HTTPS for the feed links. So, it seems none of that mattered. Only the Joomla cache made a difference.

If Joomla! has already downloaded corrupted files, so it makes sense that deleting the cache reinstated the module's functionality.