Perhaps by providing some identifier in the URL?

ie. https://10.0.0.1(af81afa8394fd7aa)/index.htm

The identifier would be generated by the certificate authority upon your first request for a certificate, and every time you renew you get to keep the same one.

I see what you're getting at - but to me this sounds almost exactly like just using DNS, even if the (A/AAAA) record you want to use resolves to an un-routable address: https://letsencrypt.org/docs/challenge-types/#dns-01-challen... - you just create a DNS TXT record instead of them trying to access a server at the address for verification.