Thanks! I ended up booking with a company who guaranteed we could fly with the doors off.

Edit: I might cancel my heli booking. For 50$ more, I can book a full daytrip to Lizard Island, which includes a 60 scenic flight over the Great Barrier Reef. It would be aboard a plane and I couldn't open any windows, but I think I could still take some good pictures, and have a lot more for my money.