FP, hi again. I've just been for a sweep too, which was unsuccessful as doc couldn't reach my cervix. Today I am 40+11 (from scan date), 40+6 (from conception date) or 40+4 (from LMP)! Doc at first was v keen to book a date for induction, but I explained that I wanted management instead, especially as my dates differ.
I had a CTG and everything is absolutely fine, so I have an appointment for Friday for a scan and another sweep attempt.
Are your dates spot on? As others have said, you can refuse any treatment, and request monitoring instead. THEY may not want you to go over 12 days, but what do YOU want? I am even more determined to stick to my guns and refuse induction after a friend was induced this week, had a horrendous long labour and ended up with c-section anyway.
Of course, if management/scans show up any risks whatsoever, I wouldn't hesitate to be induced. Similarly, if it looks like my body is ready to go anyway, which it isn't right now, I am much more amenable to kicking things off with a little help. It seems to me some babies just take a little longer to get themselves ready to come out, and we should give them a decent chance to do that!
Sorry for long post and good luck!