Any chance you've defined the new networks as "internal"? (using docker network create --internal
on the CLI or internal: true
in your docker-compose.yaml).
Because the symptoms you're describing (no connectivity to stuff outside the new network, including the wider Internet) sound exactly like you did, but didn't realize what that option does...
If you don't mind using a gibberish .xyz domain, why not an 1.111B class? ([6-9 digits].xyz for $0.99/year)