Forced into C section after planning for natural birth?

I am 40 weeks and 5 days with baby #1. Had membranes swept 3 days ago and nothing has come of it. 3 cm dilated and 70% effaced at my last check up. So worried that my body will refuse to begin labor on it's own! My birthing center won't allow me to use their facilities if I go past 42 weeks. I'll be forced into the hospital with all the interference and inducements that comes along with doctors... Do ya'll have any stories were this happened and everything turned out ok?