For three years I was working in California, but reported remotely to people in Washington DC, and also Australia. Here's what I did:
I worked the same days as the locals (SoCal) so I had some quality of life. Mondays would be busy as I caught up on the extra day that Australia had been working so I kept that day reasonably free of other meetings etc. and just focussed on responding to all of the 'urgent' email requests.
If there was a local public holiday I would take it, but just give my counterparts on the West Coast and in Australia plenty of notice that I wouldn't be in the office. They did the same. It worked fine.
I would schedule telcons with Australia and West Coast for the same day each week so that expectations were clear. Trying to talk on the phone in a unscheduled way was just frustrating, so best to make it a scheduled thing and do everything else by email. Telcons were usually midweek, early in the day for Australia, afternoon for me. I tried to be in my office for the first 1.5 hours of Australia's workday, just in case they did need to get me on the phone for something important.
I stuck to reasonable working hours, but on the odd occasion I'd have to dial into a telecon at weird hours (like midnight). I didn't mind if this was very occasional and for extraordinary reasons, but I would not make a habit of it.
Good Luck. Sounds like a great opportunity.