i was in a similar position a week ago, 40+9 and panicking. I actually had a sweep which was successful (ish) on the tues and went into labour on thurs, she couldnt do a lot but it must have done something in there.
i eventually gave birth on 40+10 so dont give up all hope yet, it can happen once u relax and have an induction date, as the pressure is off a bit.