Make that rectangle into a component which glues to "any" face (and cuts a hole, too, to avoid Z-fighting). Make sure to set the component axes so that the red and green axes are lying on the face.
Now whenever you pull one from the component browser, it will try to self-align itself to any face you snap it to. You may still rotate the component on the face but that should not be an issue.
See attached file.
CompGlue.skp