If your only goal is working https then as the other comment correctly suggests you can do DNS-01 authentication with Let’s Encrypt + Certbot + Some brand of dyndns

However the other comment is incorrect in stating that you need to expose a HTTP server. This method means you don’t need to expose anything. For instance if you do it with HA:

https://github.com/home-assistant/addons/blob/master/letsencrypt/DOCS.md

Certbot uses the API of your DDNS provider to authenticate the cert request by adding a txt record and then pulls the cert. No proxies no exposed servers and no fuss. Point the A record at your Rfc1918 IP.

You can then configure your DNS to keep serving cached responses. I think though that ssl will still be broken while your connection is down but you will be able to access your services.

Edit to add: I don’t understand why so many of the HTTPS tutorials are so complicated and so focused on adding a proxy into the mix even when remote access isn’t the target.

Cert bot is a shell script. It asks the Lets Encrypt api for a secret key. It adds the key as a txt record on a subdomain of the domain you want a certificate for. Let’s encrypt confirms the key is there and spits out a cert. You add the cert to whatever server it belongs to, or ideally Certbot does that for you. That’s it, working https. And all you have to expose is the rfc1918 address. This, to me at least, is preferable to proxies and exposed servers.