There are timed saves and in short-cuts ctrl-s or win-s that save outside the editor, perhaps these should leak through into zen mode (they dont seem to). Keeping in mind this will save the current tiddler as a draft tiddler, because the tiddler remains in draft.
Although just leaving autosave on and installing the local storage plugin may be enough not to loose anything.
Regarding short-cuts and command passed by the zen mode plugin I was not able to identify a way to add anything without changes inside the zen mode plugin (only the escape key is “hard coded” and triggers a destroy widget action).
Maybe @BurningTreeC could add the feature or an enabler?
Regarding saving tiddler as draft tiddler, if I understood well, Telmiger approach is to close the tiddler, save the wiki then open back the edited tiddler. The only drawback is that while doing so the cursor position may be lost (this is something that I can live with).
Regarding the local storage plugin, I was never able to make it work (under Microsoft Edge): I have the status local storage access denied.
I don’t want to be cruel, and perhaps we can hack a way to a solution, but primarily we need to blame your organisation for crippling security. I have referred this to the “Security tail, wagging the dog (the organisation)”.
Perhaps you can ask for this to be switched off or get permission to use another browser without the limitation.
Can you install TiddlyDesktopTS or other local app?, but then local storage is less important.