from what i understand, each matilda resident dr. gets a certain amount of spots for their patients so they have an idea where you are on "their" list.
the first ob/gyn i saw was a matilda resident, but he wasn't confident that i would get into matilda (think he had a long priority patient list ahead of me) and suggested i book another private hospital which didn't have a great reputation. at 8 weeks, when we submitted the papers to matilda, i was told i was #14 on a waiting list that matilda rep said was over 40 people long.
about a month later, i switched to my current dr., also a matilda resident, and they switched my booking with the hospital. i got a rejection notice at that time, but my dr. just said to be patient and it would be fine. i got in 1 month after that and was super relieved! i think my 2nd dr.'s waiting list was much shorter than the 1st dr.'s.
i'm due at the end of dec and they say private hospital delivery capacity is maxed out at that time due to mainland mothers shifting from public deliveries to private. read in a paper they are supposed to be limiting the number of mainland mother deliveries starting next year, but maybe that's just for the public hospitals...
good luck and hope all works out for you!