With my second child, I went to Kimberly Negrete (Neh-GRET-ee)-- she's a Certified Nurse Midwife in a practice of OBGYNs. I exclusively went to her, didn't see any of the other Drs, so I can't really say if they are all as open to natural methods. She said she was open to me laboring and delivering in whatever position I wanted to, though I wound up feeling better lying down, so that's what I did. (I delivered at St. Mary's without medication or IV, free to move around, etc. Though they did put a hepa-loc in, just in case I needed an IV later)
She's part of the "Healthcare for Women" practice that's attached to Centerpoint Medical Center on 39th St. (by Indep Center)-- www.hbahealthcareforwomen.com
You might talk with her to see if she thinks the other doctors are as open to natural methods. She said she did circulate my birth plan to the other doctors, so they would know what I wanted.
(PS-- she was also open to-- somewhat encouraged me to, since she knew I didn't want to be induced-- wait the 2 weeks past my due date. I had my daughter 11 days past my date. She suggested we wait 13 days past before we discussed induction)
PPS-- If you need a Pediatrician, I HIGHLY recommend Allison Henschel at Raintree Pediatrics. Her bedside manner is AMAZING. She takes the time to connect with my girls before jumping in to the examination, and she is much more of a "wait and see" doctor, rather than a "lets prescribe this to see if it works" doctor.
Good luck with your search!