Dear Sébastien,
Thank you for your answer, it is useful. Now I can see that I already worked on a task even if I reschedule it and don't see the "Sched. 2x" mention. But I still have to manually reschedule the task to the next week, which is what I *really* want to avoid, even at the price of not seeing what I already did either in the form of clocking time or with the "Sched. 2x" mention (maybe this wasn't clear in my first message).
I will try to write something with my very poor level of emacs-lisp. My reasoning would be something like: "if a task that has this particular property was scheduled for being done x days ago (with x > 0), and if it is not marked DONE, then reschedule it (7 - x) days later". I could maybe include a comment saying that this task was automatically rescheduled, with a timestamp. I just hope I'm not reinventing the wheel somewhere in that process.