Is there a way to conveniently update the property values of scripts when you load a save from an older version? Or do you really need to unload the mod and the reload it?

Yes.

This is all theory, from here on out.
Thought there may be a workaround. You can detect a version change easily by using two properties, one autoreadonly (actual version) and a standard auto one (used version).
Once detected you can force a reset and thus re-initialize your script and it's properties.

Detecting a version change and notifying the user might be a good idea, regardless.

Yes and this means I will have to backup the user's data in the mod before the reset(), which I didn't really feel like doing :/

You can add a "start game enabled" and "run once" quest that runs a script OnInit that updates the values of properties in another quest/script, then stops itself. It will run once when the update of the mod is first installed.

Best practice is to keep a version number of the mod stored somewhere (a quest property, a global variable) and use that to test whether updates need to be made.