We traveled from Eastern Canada to HRC (6 hour flight). I spent 10 days there, DH and DS spent only 5 days.
I did all my monitoring locally before leaving (except for the last monitoring appointment, which was at HRC).
Coming from AUS/NZ, even though the time difference is great, you will probably arrive in the US on the same day you left AUS (because our timezones are so far behind yours). Although I would pad a day or two to combat the associated jet lag. Going back, you will probably arrive in AUS 2 days after you leave the US (eg: if you leave on a Thursday, you will get home on a Saturday).
BTW, you can check out my blog to learn more about logistics planning for remote cyclers.
Good luck!!
GZ