Hi Hedgehog,
Not long to go now at forty weeks, I've still got three weeks to go for my third baby to arrive.
My daughter's head (second child) did not engage until labour started. This is a personal opinion, but I think alot of doctors like to intervene when maybe a bit of patience for nature would actually result in the mother having the birth that she wants. I don't know about the impact of a non-engaged baby on the first labour as my son got himself organised right at the last minute, but I do know, that at no time in the UK did anyone suggest to me to have a C-section or start me off despite that he didn't engage right up until the last minute.
I'm not sure that helps but good luck with whatever decision you make and just think, not long now and you will get to see that precious little bundle.
Jools