OK! Changes are not live from behind the CDN yet but it appears to work. I updated to YTC 3.0.4, changed my credentials to a Server Key (I think I was using Browser Key before), and changed my wp-config to the new YOUTUBE_DATA_API_KEY, as per the Installation instructions on the Plugin.
Thank you very much for the quick response; as I’m the OP, I’m going to mark this resolved.
Thanks again!