Obstetrician costs in the private system

[eworc]

I just found out I am 11+ weeks pregnant last week (1st pregnancy) and the GP has recommended me a list of OBs. I have shortlisted it to 2 and have been given different quotes:

OB1
Total payment of $7000 which is broken down into 3 payments
(1) Initial consultation $300 (which can be claimed - do I claim this from Medicare or my private health insurance. How much can I claim)
(2) Week 20 $4400 (which can be claimed - do I claim this from Medicare or my private health insurance)
(3) Week 30 $2600 (which cannot be claimed and out of pocket)

OB2
I was told that the the out of pocket expenses is $2500

My questions
(1) My first call to OB1, I was told I only have to pay the out of pocket of week 30 $2600. But when I call OB1 again the 2nd time, I was told that I can only claim only partial payment (1) & (2) via Medicare which would add up to $4500 (so expensive =(. I am quite sure my private health insurance covers me on OB fees as well. Is this not correct?
(2) Seems that OB2 is cheaper if that's the case?
(3) Besides these OB fees, I know there is additional fees on top e.g. tests, ultrasound, etc. Hospital stay is additional costs too? What other costs are expected to involve generally?

Your feedbacks/comments would be greatly appreciated...thanks