My first two were also 10lbs 7oz. They both got stuck, but were maneuvered out (McRoberts maneuver) with no damage. I had an OB who knew how to handle it.
With my third, I was at a new practice with a midwife who was not comfortable with dystocia, and not comfortable maneuvering I guess. So she wanted me to deliver vaginally, but in an OR. But once I finally got my epidural, things moved quickly for me and she let me deliver right there, in 1 push. He was 8lbs 12oz, and had no issues at all. I think if I'd not been so against a CS, they could've talked someone with the same history into an unneeded surgery.
Mom to a girl - 6, a boy - 4, and Baby - 2