Hi Clara
Poor you - I went 9 days over with my first and it's horrible. I had similar qualms about induction as I wanted to use the birthing unit at my local hospital and they won't let you if you've been induced - but nor can you if you're more than 2 weeks overdue. I was offered induction for when I was 12 days overdue but agreed instead to daily monitoring from then and had decided I'd accept induction two days later if no baby (due to not being able to use birthing unit in either case). Anyway, happy to say that baby turned up when 9 days over so didn't need either the monitoring or the induction.
I had a sweep the morning that I went into labour (last Monday, 8 October) at 9.30am - had had no signs of labour prior to this and was only 1cm dilated. Midwife also suggested alternative methods including reflexology and recommended a reflexologist who specialises in this (she used to be a midwife) - had the session at 3pm, went into labour 8pm and my gorgeous baby girl arrived at 10.21 the following morning - couldn't quite believe how quick it was. Had a great birth, was able to use birthing unit and pool. The reflexologist told me that she has a 75% success rate when combined with a sweep - midwife also suggested that if reflexology didn't work, then acupuncture was possibly more effective. So, maybe worth talking to your midwife to see if they have any suggestions?
Very best of luck - I know it's frustrating, I was going mad the first week, but worth the wait. One other point is that I'd had an inkling my due date was out by a week or so (I don't have a 28 day cycle) and the midwife who delivered my baby didn't think she was overdue as she still had a lot of vernix over her - so there may be some margin for error there.
Hope all goes well for you!