Can you run two instances at once? Bring up new on different port, switch nginx proxy config to send traffic there, bring down old…
And for true zero downtime, maybe use Envoy instead of nginx, since Envoy does some serious hot-restart magic where it will hand off existing connections to the new instance 
There are plenty of solutions to bypass the problem I’m tackling (like the one you are offering), yet in that case, I want specifically to try to solve the systemd activation thing & see if we can make it work.
Doing this because I think nginx + systemd will remain quite a common solution for entry-level deployments.
Thanks for the proposition, though, this is still helpful (& feel free to share your Envoy setup in a separate thread, by the way, it can definitely be interesting!).
I do the same (Docker Swarm built-in rolling deploy on a single node) for a Go & Python app and it works really well.
I have checked it out, and even written and published library for integrating Erlang applications with systemd:
https://github.com/hauleth/erlang-systemd
And using that I have created example Plug application:
https://github.com/hauleth/plug_systemd_example
Unfortunately this do not implement socket activation, yet, because gen_tcp and gen_udp require unbind(3)ed file descriptors, and when you want socket activation then you (obviously) will get file descriptor that is already bound. However there is some hope in form of socket module and moving from init to it. When socket will get a way to use existing file descriptors and there will be a way to “create” gen_{tcp,udp,sctp} out of such existing socket then it will be possible and I will try to extend the example to use it as well.
Right now the available features in the library are:
Ok, I have found a little bit tacky solution that I have described in my post about systemd library: