For internal use, create and distribute you own root CA with self-signed certificates.
ACME would be ideal, but the official response of Let's Encrypt is that ACME is overkill for corporate environments and you should roll your own certificate automation.
At one place we aggressively policed external facing certificates. Don’t follow the process, your service gets whacked.
It’s a process you should look into, because the compliance regimes will start paying attention to it someday soon.