I know how hard it is to get information in the city when it comes to Obstetricians practices, C-section rates and Vbac rates. So through the years, having worked as a doula in most of NYC hospitals, I have compiled a list of the best Drs in the city when it comes to natural birth and very low intervention rates. Drs I know for sure will support a natural birth - for having witnessed it.
These OB/GYNs will use intermittent monitoring, let you labor in the shower/tub and walk around provided you are low risk. Their induction rate is also very low.
NYU has an 98% epidural rate