Using wildcard certs and/or a central reverse proxy defeats the purpose of internal TLS.

Split-horizon DNS for a publicly usable domain is almost always a bad idea, but running your own ACME server is pretty easy (maybe 10 lines of Caddy config) and using an internal domain (an actual one, not a randomly picked TLD you don't think exists yet) solves the problem pretty easily. You'll want a safe backup for your root certificate private key, of course, but that's pretty much all you need to really worry about.