I have trouble with short posts
Sorry, but I thought of something else
I've just read Birthing From Within by Pam England and Rob Horowitz (our library had it). It's a very interesting and beautiful book and it talks about the changes in pelvic diameter in the squatting, semi-sitting, and lying flat positions. It says that while lying flat works against gravity, may decrease oxygen to baby, and may increase your labor pains, it is actually better than the semi-sitting position (which sounds like the position you were in?) because semi-sitting decreases the diameter of the pelvic opening more.
The same page goes on to say that CPD (Cephalo Pelvic Disproportion) wherein the baby is too large to fit through the pelvis is a common explanation given for Cesareans but is not an absolute diagnosis and that such women often birth larger babies naturally in subsequent births.
It makes me mad if your doctor did tell you this without due cause, because it could effect all of your future births and cause unnecessary trauma to you and your babies!
Oh, while I'm recommending books, Spiritual Midwifery is my very favorite birthing book, full of birth stories of natural births, several of which were "supposed" to be impossible or dangerous. It's very spiritual and a heartwarming read
As an aside, when I delivered my daughter, her head came out but her shoulders were stuck (shoulder dyscotia). The midwife had me turn onto my hands and knees and pulled her out safe and sound with no bruising. I don't know how that relates to your experience, since my daughter's head was actually outside of my body and looking around by then . . .