How to start a shared X server for remote, non-forwarded use?

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I am not sure I am asking the right question, so here's what I actually want to do:

I have a server that has a screen coected to it and no other devices. It is ruing an SSH server.

I would like Alice to be able to coect to the server and run a command as "staff" to show a picture on the screen. For example...

ssh server sudo -u 'staff' gst-launch-1.0 playbin uri=file:///path/to/image.png

Alice goes home, and the image is still showing. Bob comes in, and decides he wants a different image:

ssh server sudo -u 'staff' gst-launch-1.0 playbin uri=file:///path/to/other.png

How does the X server need to be started and configured to meet my needs? Only the "staff" user will need to manipulate the display.

I know that I can start the server on boot using xinit and run a program of my choice. What program should I run? What should it do? Are there environment variables I will need to pass around?