There have been some good ideas thrown your way- staying home and cancelling appointments, changing providers, and spinning babies, etc.
I have some things to add, some may be repeats, others you may choose to ignore. I am going to put it all out there, and let you sort through it. I do not have the energy to try to be nice or PC. I am sorry if anything offends. I do not mean to.
Cytotec should NEVER EVER EVER be offfered for induction. If you have done your research at this point, you will have seen that for yourself. So, while I know you are saying you will refuse this route, it also begs a different question: what kind of care provider is this to be recommending something that can/has killed mothers and babies at a higher rate than acceptable? What are her other practices that you haven't found out about yet? She is not putting your or your baby's safety at the foremost. Do you trust her then as a care provider?
It is NEVER TOO LATE TO CHANGE CARE PROVIDERS until the baby's head is out. It takes gumption and resolution, and strength. But is better at times than the other option.
You also say that you are sure your dates are off. Your care provider is refusing to listen? That is not a good midwife. Period. A good midwife is guided by the mother's wisdom. You are the expert on your body and your baby, not someone else. They are there to serve you, and help provide you with accurate information, and also to listen to you. Regardless of whether you buy time with the date issue, you may very well still be in this situation 10 days from now if your baby is not yet ready to be born. So do not think that dealing with this date thing alone is the solution. You may still have more ahead of you. Do you want a care provider that does not listen to you? I had a freind who knew something was wrong with her baby... her care provider refused to listen. The baby died. Not meant to scare you, just that I think our primary reponsibility in birth is to listen to the mother.
As far as induction: Right now I will be honest. You have NO MEDICAL REASON to warrant induction with any thing- not pitocin, not cervidil, not even herbs or castor oil. There is nothing wrong. NOTHING WRONG! Your body is not late, your baby is not late. In fact, your baby cannot at all read calendars. Do you have fruit trees? Some fruit is ripe before the others. Some will be the last to fall. On the same tree! What you are dealing with quite frankly, and I am sure you are smart enough to know, is an issue of politics and policy. That is the reason for induction. If you have researched induction of any kind, you will know there are very real risks. I hope you have your copy of Goer's Thinking Woman's Guide to a Better Birth.. Labor happens when it is time. It has for eons. No one ever walked around pregnant forever. I hope you can protect yourself enough to avoid a non-medically indicated intervention.
Moreover, if indeed your baby is posterior: Do you KNOW THIS? If s/he is posterior then you DO NOT WANT TO INDUCE LABOR BY ANY MEANS! You know this by now, right? You need to get the baby into an anterior position, and then the bbay will be able to do the work of birth. Of course posteriors are born if left alone, but why ever should a woman knowingly induce one? Go get in the water. Don't sit on anything other than a birth ball- scrub your florrs, spend time all day on hands and knees... if your care provider is not good at palpating- maybe you are, or is there a HB mw around? Perhaps she could verify position?
AND PLEASE LISTEN UP: DO NOT DO ANY SQUATS until you can confirm that baby has rotated anterior. You do not want to have a posterior baby drop (which squatting will encourage) and be locked into a non-optimal postion for birth. In fact, if the baby is low right now, and posterior, part of what you may need to do ifs knee-chest in order to get the head unengaged before it can freely rotate. BUT PLEASE DO NOT SQUAT until you know it is not OP.
I do not mean to yell, just this is so long winded I want you to be able to see the really important things.
I am furious. Not just for you, but for all women, and our babies. I am so tired of women thinking their bodies are broken, incapable of going into labor.
You are a mother, a woman. You are designed perfectly for birth. You are to be honored, and listened to, and empowered. You still have options. Rise up, woman, rise up!
I know you are tired, and want to see your baby. You will. In time. I wish for you something different than all those posters who hope you go into labor soon. I hope for you that you claim your power. I hope for you that you have attendants that honor you and listen to you. I hope for you that your baby is born gently and easily- in his/her own perfect time. And I hope you share that gift of unfoldment with others... whatever that means.