D.B.
If you have no other alternatives, I would recommend that you pay the midwife out of pocket. If you have a serious problem and end up HAVING to go to the hospital, you'll be covered for the extra expenses. Make sure you have that contigency lined up.
There's another poster here, Pamela, who was adamant that she would not have a hospital birth either. However, nature didn't work with her, and it turned out that her baby was far too big for her to birth vaginally. She and her little boy would have died if they hadn't gone to the hospital. I've never met anyone more opposed to a hospital birth than Pamela, but she and her midwife knew when to throw in the towel and protect their lives. That's what you need to be prepared to do too, if it comes down to it.
In a case such as this, your insurance will be a financial lifesaver for you. It's a shame the $4000 won't be covered, but at least you have a cushion beyond it.
Have you written the insurance company a letter? If you try to get permission outside of the regular rules, maybe you'll get somewhere. You have some time to work on it now. Get a lawyer's help, if you need to.
Good luck!
Dawn