…turned out to be much easier than I would have hoped or imagined.
The only thing to remember is: drag the current widgets into “inactive widgets” area before messing with themes. This will make sure that your customizations will not be lost (like custom title for a widget, or custom text, or settings e.g. the number of last tweets to display).
I tried it for my self-hosted blog and yes, it worked! The theme re-install also resets all of the code customizations. I previously had written custom text for the error page (which I saved in a separate file in order to preserve it), and also had a custom way of displaying page titles (which I will have to google again, if I decide to do the same thing with the current theme).