hi - my ds has a big head (!!) just like his mama lol.
He was born 18 days overdue by my LMP date. However, if they had gone by my scan date, he would have been 25 days overdue. In reality, as i know EXACTLY to the day, when i conceived him, he was born at exactly 40 weeks from date of conception (so if you add on the normal 2 weeks for EDD he was born at 42 weeks).
I knew in my heart of hearts that everything was ok - call it intuition !! therefore i fought to the 'death' to wait and not be induced. I was very anti induction, as i wanted a natural labour at home. iN THE end i didn't have the energy to fight for my home birth, but got my natural labour at the hospital instead.
DS was born quickly, easily and without and drugs, so was v alert and relaxed, bf v easily and is quite advanced for his age (5 mths) and very large - 95th centile. No vernix or hair or anything. However, he was born with a ridge on his head, which makes me think that he was in the wrong positon - so if they HAD induced me, i would have wound up forceps / ventous / c sec which i didn't want.
i had monitoring every day from 12 days overdue, which was fine, but when i eventually went into labour i had to fight to stay OFF a bed and on my feet as they wanted me strapped to a monitor so they could tell very quickly if there were problems. In the end, he nearly birthed himself it was so quick - the midwifes didn't enter our room for an hour so me on a machine would have been useless because they wouldn't have known of any problems anyway !!
There is alwas a risk (meconium, placenta depreciation etc) of going overdue, but i think that i naturally cook babies longer as my cycles is 35 days on average. I would go with your instinct but grab at any monitoring opportunites and be armed with lots of ammo as they like to resort to scare tactics.
Homebirths.org is a v good site for stories of going overdue and being ok !!