Hi,
Yes we have used nsenter to enter a running container - using also chroot (in /usr/local/var/singularity/final... )
Just download/install a recent version of util-linux (2.28+) to use lsns and get your process ID for the wanted namespace.
I don't know how you want to mix this with ssh but anyway you can install openssh-server in your container and then you can login in it.
But singularity should not be used to run service b/c it won't be close when you will stop/exit from it. Indeed, like Greg said, you can look at Michael Bauer code to manage more gracefully your container as a service. Scripting the daemon should not be too tricky...
Best regards
Rémy