A DNS Proxy/Forwarder server? That’s where you would configure how your .internal domain resolves to IPs on your internal network. Machines inside the network make their DNS queries to that server, which either serves them from cache, or from the local mappings, for forwards them off to a public/ISP server.
rsync, for sure. That’s what I used when I had to migrate a 10TB datastore to a new machins.