Hi Susan,
Are you looking to birth at a hospital, at a primary birthing unit or at home? I am planning on birthing at Birthcare in Parnell and they have two teams of midwives (3 in each I think) who provide LMC, so that is what I decided to go with. You meet a different midwife at each appointment, so that you get to know them all. I was my sisters birth partner with one of their midwives and she was terrific, so I decided that was the experience I wanted. As a primary birthing unit they are pro-natural birth (although will transfer you to Auckland if there are complications). I think they still had spaces for March, might be an option for you if you are struggling to find an independant, but I'd contact them asap if you were interested.
Good luck with whatever you choose to do