Managing Steam game saves in gaming arcade environment

I am in the process of researching the viability of a VR gaming cafe. Since this would largely use games from Steam, I am looking at the capabilities of the Steam platform and what it allows.

I am aware of the Steam Site Licensing Program which appears to suit the general need to have a centrally managed Steam account without requiring users to log in to their account.

One problem I've run into, however, is how to manage saves for larger games. Particularly as games like Doom VFR and Fallout 4 VR come out that would require multiple play sessions to complete it seems important to persist saves per user somehow.

Is there any way to manage saves per user per game? One method I thought was to copy the local save to a central storage server after the session is finished, and copy it back for a specific user when the game is relaunched. This seems a bit cumbersome. It would be nice if there was a more concrete way of managing this.

Are there any good ways of managing saves in a gaming arcade environment without users logging in to their personal Steam account?