Well, that was exactly my situation with DD, she couldn't descend properly because of having the cord wrapped round her legs a hospital record breaking 8 times. It wasn't dangerous for her, other than there was only one way out and that wasn't the natural way.
I insisted on scan with DS, but they would have done it anyway cos of history. They measured him, he was a whopper and I had too much fluid, so they insisted on c-section. I was pretty devastated to be honest, as was so desperate to "do it properly" but when it was all over, I realised I wasn't really bothered at all. I cracked the BF second time round and that seems to heal a lot of old wounds.
I'm also a tummy sleeper - I couldn't sleep without my big V pillow I got from John Lewis - do you have something like this? You may think it's a bit late now but anything to help you get a bit more sleep before the big push....It's like a really long sausage pillow filled with microbeads. I used to lay on my side cuddling it - my top leg rested on top of it, if you see what I mean. I saw me through to pregnancies, hospital stays and feeding newborns (even used it when formula feeding DD as both babes were heavy at birth).
It's hard to know when to refuse an induction - you'll be better informed if you have a scan. I had high BP, so they started inducing at 40+ 7 - I actually eventually had her by EC at 42 weeks. After being put on the drip in the end. I guess they needed to go through all that to realise she wasn't coming out, but it's a shame because it exhausted me and she ended up in foetal distress - hence the EC.
Maybe give the pillow a try, but also try and get scanned before you have to try and put your foot down about induction - it's emotive - I had done NCT course and was so indoctrinated enthusiastic about a natural birth that I don't think I had great perspective on what might have been best for safety of me and the DD. To be honest, I felt like a failure for having (literally) every intervention on the planet, and then ending up with a section. I was literally blubbing on the floor of the antenatal ward begging them to let me in the birth centre - it was like being barred from the most precious club in the world!
So I suppose I'm saying, stay focussed on the birth you want, but get the information you need to make the best decision for you and your LO.