Dan Byler's
Defer script does much of what you want. You can defer a project and its associated actions by an integer number of days (use a negative number to move something forward in time), and it will do multiple items at once. You can change either the due date or the due and start dates, though there is no support for moving due & start dates different amounts. Invoking the script twice would accomplish that, however.
I've noticed that the script works best if you make your selection in the right-hand pane, not the sidebar, and if you want the included actions changed, they need to be selected as well.