OP, YANBU. I totally agree with you that induction has associated risks that are often ignored whereas the risks of waiting to go into labour spontaneously are highlighted.
In your position I'd be asking for extra monitoring, including scans to check blood flow to the placenta and amniotic fluid levels, etc.
There is some evidence to suggest that sex helps to kickstart labour (and it worked for me!) so why not try it, worst case scenario you have some fun while you're waiting 
Do be aware that when you go significantly past your due date, there is a chance there might be meconium in the waters. This isn't always a sign of distress( it can be, but in post-dates babies it can just be a sign that the bowel has matured and they're ready to start filling nappies! However, it does mean they'll want continuous monitoring during labour as there is a risk of meconium aspiration if baby does get distressed.
I gave birth to DC1 at 41+4 after going into labour naturally. I'd had a sweep which had done nothing, acupuncture which was relaxing but no immediate effect, then sex did the trick! I did have meconium in the waters but DS was fine.
I didn't want an induction but would probably have consented to one at 42 weeks. I wanted to be in the midwife-led birth centre but they only allowed it up to 41+6 and from 42 weeks I would have been on the delivery unit anyway, so I think I would have accepted defeat at that point and tried an induction.
No judgement for women who choose to wait longer though, or indeed have an induction sooner. It's just a shame women are not trusted to make an informed choice and are often pressured by HCPs.
nurserypolitics
"I was then overstimulated by the pessary, they had to take it out, DD was very distressed but it resolved. However it was a pretty awful labour: I experienced it as one long contraction, no breaks. Then, when I finally got to 3cm, they were again concerned about her heart rate: I had an epidural, waters broken (Meconium in waters)and the drip. Her heart rate went funny again, as I reached 10cm, and had instrumental delivery to get her out fast."
After all that, do you really think it was the length of gestation that caused your baby to get ill? Nothing to do will all the interventions during labour, baby's distress, and the increased infection risk of doing VEs and other internal interventions after waters have broken?