'/.well-known/pki-validation'
For the wildcard certs, you just need to add a TXT record to the public DNS entry, no public web server required.
Even if you have no intention of using your internal DNS domain name on the internet, it's good practice to register it anyway.
The problem here is that there's no such thing as domain ownership, only domain renting. You forget to pay your bill (read: someone loses an email) and a core part of your infrastructure is up in smoke, or worse, taken over by a squatter.
I don't think there's a way around coming up with a reliable process for renewing your domain. You somehow manage to do it for lots of other things already.
See eg point 4: 0https://github.com/Neilpang/acme.sh/wiki/How-to-issue-a-cert
Most clients that support DNS-01 can use nsupdate or APIs of public DNS providers to make this an automated process.