There are no special tables or anything it needs as everything is read from your Cloudflare account. If it was working before the domain changed, you might want to remove the token (save it as an empty value), reload the page to make sure the token is gone and then put it back in. Internally it *does* save the Zone ID (which corresponds to your domain) when the token is added. Maybe it’s somehow mucked and trying to use the old zone ID for the new domain?
Beyond that, it’s perfectly safe to delete/deactivate the plugin and then reactivate since all the Cloudflare related stuff is coming from the Cloudflare API.
Still confused on what would be causing those settings to be greyed out… there’s literally nothing that would grey those settings out… so there’s something going on outside the individual settings (can’t imagine what though).