I concur with almost everything that's been said here. Do *not* use cytotec, it is not approved by it's own manufacturer for the use of cervical ripening. Why are they even using this? Even a small dose, I wouldn't use ever. There are a lot of other cervical ripeners. Google Bishop's Score Chart I believe it's called and that will tell you how likely you are for an induction to work.
A membrane sweep is not an irreversible induction. The risk is that they might puncture your bag of waters, which is a risk. I go past my guess date with my babies, finally after baby #3 I figured out why, asynclitic head.
My first ds my OB did a very gentle sweep I believe without my knowledge when he did my vaginal check (didn't realize how pointless those were at the time) and that got me going. I had ds 3 days past my "guess date."
With ds#2 I had a diff. practice and the CNM was threatening induction as I was 8 days past. I would not consent to set up an appointment so she offered as I was walking out of the office to do a sweep. I went ahead and consented (Btw I have a lot of early labor on and off-"prodromal" labor) so I was 3-4 cms already and 80% effaced. She did a very aggressive sweep, ouch, unlike my first and I was in labor by the time I walked out of the door and over for my NST. I remember telling the nursing staff that I would be back later that night, that I was in early stages and they rolled their eyes at me. I had my baby that night at 11:51 pm.
With dd I had a homebirth and she was 10 days past. I was getting all of the same advise and I know the same advise I've given to students. However, I felt in my gut that this baby was over, fine but over. So dh and I had sex that morning, I sat there after holding it in....sperm is a natural cervical ripener..for a good 5-10 min.s Then I did a lot of walking that day, endlessly. I hit early labor that night around 6 pm and had the baby by 6:30 am with active labor hitting at 3:30 am. I did some moves to help the baby's head line up just before 6 pm and that helped tremendously (like doing a pelvic rock during a contraction) and sitting with one leg up while the other is in a kneeling position during a ctx as well, and a belly lift during a ctx- they all worked.
Chances are just let your body do it's work and the baby will come when it's time and that's probably very soon. You can try some of the other natural inductions (like sex) and if your body is ready then it will take. Same with a sweep, if your body isn't ready then it won't take but if it is I think it's much gentler than pitocin or heaven forbid cytotec.
Best of luck. Can't wait to hear.