Hey J.!
I'm a Doula (professional labor coach) and I encourage you to try to avoid induction at all costs. Ask the doctor about the drugs he/she plans on using for cervical ripening and google them to find out any issues. I won't waste time going on and on about inductions here, you sound informed already. If you need more info., google some or hit a natural birth website. The best way to avoid an c-section is to avoid induction.
Don't worry about baby not fitting in your pelvis - that is so rare it isn't even funny. The docs use that as an excuse all the time but it's really caused from having a woman push while on her back. That actually makes your pelvic opening smaller!!! Duh! I recommend pushing on your side or best of all hands and knees (squatting/standing good too).
Baby may not be dropping due to position (like other poster said). She may be sunny-side-up (nose facing your front)or her head mayb be at a funny angle. So, to fix this you need to spend LOTS of time on your hands and knees doing pelvic rocks. This position uses gravity to pull her away from the pelvis and give her the room she needs to position herself correctly. When on your hands and knees, hunch your back up while pulling your pelvis in (pelvic rocks are hard to describe! LOL) and then release back to having a straight back (don't let yourself get a sway back, keep it straight). Also, wiggle your hips around and anything else that feels good. All that movement gets her going too. Have a little something sweet, like juice, before you start to give her a little more energy and try it for sure when she's awake and kicking.
If you go into labor and have tons of back pain on one or both sides, you can be sure she is in the wrong position. You need to be on your hands and knees during labor to get her to change. She can be born in that position but it is a lot harder and longer labor. Many section happen because of this position.
If you would like to talk on the phone let me know - I'd be blessed to help you in any way I can.
Kind Regards,
Amanda