You have correctly answered your own question. Docker creates its own network to allow communication between containers. By setting networking to host, you tell docker to link the container’s network interface directly to the host machine’s, excluding it from the docker network.
You can map all the ports you need accessible and tell the container to use backend to get what you want. This is how I have mine setup so I have a minimum attack surface on the server.
I can’t give you exact examples because I’m on my phone, but have a look at the ports section of the docker-compose file reference.
You’ll want to map "8443:8443" and probably "8080:8080" as well.
When you are on network host mode you can’t / don’t have to do a port mapping.
If your influx is running in a internal docker network you have to do a port mapping for that container to make sure that port 8086 is an external port (known in your host network)
I’m a bit concerned about security (a container in backend exposed to host network), but I don’t think there are too many options …maybe some security config I’m not aware of?