T.H.
I've had many (almost 100) great birth experiences at Huntington as a doula. I don't know what you mean about being rigid regarding inductions -- only the doctor can induce your labor and the hospital has to follow the doctors orders. Huntington is a very birth friendly hospital with fabulous nurses! The only negative thing about Huntington is that the partner isn't allowed into the nursery with the baby! Since you don't have to allow your baby to go to the nursery, it shouldn't be a problem.
Drs. Parks, Tamayo and Yun might take your insurance and they're awesome doctors :)