"I think you are missing the point of SSL certificates with Solr. They are not just used to encrypt the connection, but they are also used for Authentication. Self-signed certificates work exceptionally well in these situations, and this security model is used extensively throughout open source and commercial projects."
No, I'm not. Solr uses Basic Authentication, configured separately / independently from the SSL certificate. As I indicated at the start, the Solr self-signed certificate was blocking web browsers from accessing Solr on my domain.