I had something similar to this with my most recent birth. Because the baby had anomalies, it wasn't perfect, but it was still so different than my first two c-sections. I got to hold Psalm in the OR on the table for a long time, and take her with me into recovery. And my midwife (a CNM) was able to scrub in and act as my nurse, so I still had that good support. Here they call them family centered c-sections (which I think is more accurate a label than "natural"), and they are actually now the norm at the hospital at which I deliver. (St. Luke's Baptist)