My doctor did would only do inductions past 39 weeks. When I was 3 days overdue I asked to be induced but luckly I went into labor on my own that morning and was sooo much happier. People freak out about inductions.. I believe if you want one go for it. But your case I think you should wait a bit :) labor always comes eventually haha
I would have thought they should wait unless there were a reason, its around 14 days after your due date that the placenta would start to deteriorate, they normally start induction at 10days past or so.
Personally, I would ask to push it back a few days or so, inductions dont always go too well, I was 4 days overdue with my last baby and we had a perfect labour and delivery, I cant say the same about my first who was induced at 4 days over. I would ask for another sweep, it may just be enough.