FYI you can now do this with the new “Set a date field” rule action in our Flowsana integration. It’s a little bit of an odd-looking usage of it:
You’re setting the due date to the same due date, but the key is the “Skip weekends” checkbox which will move it off of a weekend day if you change it to fall on one.
(Also note this will work when changing the date in any view, not just the Timeline.)