Hi! I'd like to help you connect the two services (Docker-Mail and your forwarding / delivery service). It's great that you want to leverage Docker to provide support for both use cases!

Because Docker is a container-based platform, you can deploy a new instance of the Mail server within one of these containers, which means it’ll run within your Docker host without having to set up another machine. It also gives you flexibility in terms of configuration and customization – each mailserver runs on its own dedicated IP address, which makes it much more powerful than using the Gmail API or other common forwarding services that work via email protocols.

Now coming to your specific situation, there could be a couple of reasons you’re looking to set up Docker in your environment:
1. Security concerns (more secure and controlled system).
2. Ability to maintain custom configuration/settings.
3. To keep all settings in sync and manage from one place instead of having to manage them each individually in different locations.
4. For load-balancing and easy scaling – Docker makes it very easy to spin up new instances without the need to worry about setup and downtime. 

Here’s an example configuration of your forwarding / delivery service (you can adjust the ports as per your preference):
```yaml
version: '3'
services:
  dockermailservice:
    image: myorg/docker-mailserver:latest
    container_name: myorg_docker_mailserver
    command: ["--port", "1120", "docker-mailserver", "forwarding"]
    networks:
      default:
        ipv4_address: 172.18.0.3
    volumes:
       - "/etc/nginx/conf.d:/etc/nginx/conf.d" : /usr/share/nginx/html/:/etc/nginx/
    depends_on:
      mailserver:
        condition: service_healthy
```
- `command: --port 1120,docker-mailserver,forwarding` tells Docker to use the container's ports 1120 to expose it on the local machine for web traffic. 
- In 'networks':, 'default' and '/etc/nginx/conf.d', volumes will mount the mailer folder on host from the container and host file mapping to your forwarding service on the local machine. 

Forwarding Docker mail to an SMTP server via Postfix is a popular way of achieving this kind of configuration and has great integration with other tools like Dovecot for sending emails. Here’s how you might achieve that:
```bash
docker run -d --network mail_net --name my_mail -p 1123:113 --volume /home/dockeruser:/mnt -e DOCKERMAIL_CONFIG=/etc/master.cf myorg/postfix:latest
```
Note the command-line flags, `-d` (Run in the Docker daemon), `--network` (Name your network) `mail_net`, `-p` (Port binding for local use), `-v /home/dockeruser:/mnt (Volumes for host directory to /var/mail on the Docker container. Use the exact path, because the docker API treats / as a relative path - this makes things work faster. In production, you may want to map host directory into Docker and then bind-mount it into mail_net so your volumes don't collide), `/etc/master.cf`, myorg/postfix:latest for Postfix service.
Also remember that running docker containers on port 1123 may result in binding the port number to the local IP address (0.0.0.0), this can affect performance when multiple containers are trying to access your mail server at the same time.