Please don't be hard on yourself OP.
My first was born on his due date, so I expected my second to be early. He wasn't.
Every day that went by I got more and more frustrated. In the end I had a nice warm bath, a nice drink and went to bed. Labour came that night, I think because I had given up and relaxed, but who knows.
I had water births with both of mine, I was very lucky. I would also have delayed induction, it was an absolute last resort for me.
The WHO states the average length of pregnancy is 37-42 weeks. It has been known for babies to come as late as 46 weeks naturally (not that you will get there, but just emphasising that this could be completely normal for your body and baby). Your trust aren't being supportive and should be offering additional monitoring if you decide you wouldn't like an induction. There are absolutely circumstances where medical induction is necessary, and we should be grateful for that as a society, but I don't think they should be pressuring so much purely because of due dates. There is a slight increase in stillbirth rate, but it is nowhere near as high as I've heard it made out to be. Something like 0.05% risk to 0.5% risk. That's an example though, I don't have the exact percentages to hand. It does not mean that your baby is going to die, just that the risk is ever so slightly higher.
Perhaps ask them for evidence that your baby is at risk, and if there's anything aside from due date there isn't anything to suggest you or your baby are in danger?
They don't consider induction in my trust until 40+10 and some trusts are as late as 40+14.
Have a little google of AIMS (Association for the Improvement of Maternity Services). There are a few downloads on there about induction and also your rights (I think that one is called 'Am I Allowed?'). I've found their website very useful in the past. Also have a look at the WHO for information.
The decision on your care lies with you. The doctors and midwives aren't responsible for your birth, but they are so buried under guidelines, targets etc. Do some research and question them. Work with them to have the best birth for you. You and your midwives/consultant all want the same thing - a healthy baby and a safe delivery.
Additionally, a consultation on the phone or in person with a private midwife could be invaluable at providing more reassurance, as they have time to explain and go through your concerns. Unfortunately our NHS staff are under so much pressure they really struggle with time and sometimes explanations.
Best of luck and wishing you well. It won't be long and you will be holding your beautiful baby 