The problem with a different spoof for each domain is that this behavior on its own can be used as a fingerprint based on timestamp and IP in access logs.
Hiding among the crowd is probably better, especially since newer versions of Chrome all report the same UA you blend in even more.
With Docker, the internal network is just a bridge interface. The reason most firewall rules don’t apply is a combination of:
The only thing that should be affected by the host firewall is the proxy service Docker uses to listen on a port on the host and send it to the container.
When using Docker, each container acts like an independent machine, and your host gets configured to act as a router. You can firewall Docker containers, the rules just need to be in the right place to work.