This was developed using git v1.8.3.1. From git v2.3.0, the use of the GIT_SSH_COMMAND environment variable instead of leveraging ~/.ssh/config.

Make your ~/.ssh/config file look like this:

UserKnownHostsFile /dev/null
StrictHostKeyChecking no

Host mygitserver
    Hostname localhost
    Port 2222
    IdentityFile ~/docker-git-server/keys/id_rsa
    IdentitiesOnly yes