E.S.
Homebirth is probably the cheapest way to go (even out-of-pocket) ...as there would be no "facillity fee", as with a birth center. That is what got us last time, even when we had insurance that paid for almost everything else. Independent midwives seem like a flexible bunch...mine will do payment plans. I imagine there are others who will as well.
Experienced midwives also know a bit about billing issues, and which insurance companies are more generous. Good luck!