We used midwives both times - once a nurse midwife in a hospital and once a certified midwife in a freestanding birth center. Both were covered by our insurances (different insurances from the first to the second). Actually they were covered 100% - we didn't pay anything. No, I take that back, we did have $10 copays with the nurse midwife but nothing at the birth center. I know we saved the insurance company many thousands of dollars by birthing out of hospital. It was win-win!
Call and check with both your insurance and the midwife practice you are wanting. No, it not too late to switch - you still have over two months to form a relationship with the midwife. But I would switch right away as you want all that time to get to know her (and her you) better. I did not read your birth plan post - what happened? Or just tell me where it is posted so you don't have to retype!
Having used midwives, I would never have a doctor unless there were some serious problems - and even then I think I would use a midwife with doctor backup. It is your birth! Utilize care that makes you feel respected and protected! Fighting for the birth you want is not what you should have to do - your birth attendent should have similar views to yours to begin with!