Agreed that policy is super strict - it's a great program but I guess they really don't want to do anything to jeopardise the program so they seem a bit nervous when it comes to policy. You really will need to be super low risk.

When are you due? They fill up pretty fast, so my advice would be to have your booking in appt, ask lots of questions about the homebirth program, and then decide from there if it happens to be offered to you. For what it's worth, if I could afford it I'd probably choose private over public, just for (as the others have said), someone who works for you, and not the hospital.
All the best with deciding (and congratulations).