When I was pg with my son I found myself in a similar situation in that a lot of the "good hospitals" especially the birth centre filled up so quickly that you basically had to book in the moment you peed on a stick. I remember going on a tour of the birth centre at 8wks and being told that they were pretty full and if I wanted to birth there I would have to book in pretty much that day. Luckily I found another hospital that although wasn't a birth centre was actually a lot more relaxed and had a less medical environment and had a beautiful birth there so hope it all works out for you.