I can not recommend enough the place where I had my daughter. It is called the Birthing Cottage of Winter Park - 434 Grove Avenue, Winter Park, FL 32789 - ###-###-####. They accept all sorts of insurance including Medicaid.
I am a mother of four children. I have a 7 year old, twins who are 3 and my daughter who is 1 1/2. Both my first and second deliveries where at a hospital and with a doctor. I know exactly what you are talking about. Its not ok and what you are looking for is not unrealistic.
I came across the birthing center and once I visited it, I knew it was perfect! They are trained midwives who have delivered hundreds and hundreds of babies. You go to the center and all over the walls are pictures of Moms with their newborns. Our picture is up there too! I still keep in contact with the woman who helped me deliver my daughter, that is the type of connection you hope to have with someone who is sharing such a personal and important moment with you and your family.
Their visits are about an hour or longer if you have questions or want to talk about the birth or anything. Its more of a conversation about you, how your eating, feeling, questions you may have, etc. My birth was wonderful. I had two midwives who were on call for my delivery and they catered to me and my baby. It is very much about you feeling comfortable as they know if you are comfortable, so is the baby, because the baby is affected by mom's emotions. Their is a whirpool for you to labor in if you want, a lake nearby to walk around.
I know it is a little far for you, but I would highly recommend to you to check it out. It sounds like what you are looking for. What ever choice you make, continue to be strong in listening to your instincts and be comfortable with your choice. Keep searching with an open mind and you will know when it's right for you.
If you want, you can contact me at ____@____.com
Best of luck to you!