Media library links are still showing up as http://xx though, so any images used on the subdomains are flagged up as insecure. Only one subdomain - our most recent one - has media library links with a structure https://zz.xx.com. It's possible that the SSL certificate was installed after the other subdomains were created, but before ZZ was: I'm not sure.
How can I get WP media library links all showing up as https:// - and preferably with the subdomain in the URLs?
Ideally I'd like to do it without a plugin if possible. Thanks!