Hey,
A girlfriend of mine had a baby by c section cos the head was no where near engaged. I think she was about a week over and they just booked her in for a c the next day! They frightened her with tales of the baby lodging on the cord etc, but having had the operation she decided to do a bit more research, and that is quite uncommon (but still a risk).

I was also surprised that they didn't induce or at least wait a week more, but I guess it depends on your OB.

The main thing is that you feel comfortable with your decision. Do your research to find out what are the chances of engagement later, what are the risks, what happens if you are induced, etc. At least if you end up with a C section you will feel informed and more positive about the experience.

Good luck!
PS I hear breast stroke is great to get bubs engaged...