My wife and I are planning to visit Bora Bora and Australia in May 2016, but I'm struggling on how best to do this with points. I believe this can be done on one award ticket. I've always used Ultimate Rewards, and have about 150k points so far saved up. However, I've heard Ultimate Rewards points may not be the best for this trip. I'm planning to broaden and increase my points accumulation through credit card offers, and can open cards for both my wife and I. I have two main questions:

1) Can anyone recommend the best program(s) for awards travel to Bora Bora that permits also visiting Australia? I've heard mixed opinions between AA, Delta, and Amex MR points.

2) Is it possible to also visit Asia on this trip? I figure I can do a bunch of one-way tickets, but then I worry I'll likely lose the stopover ability and it'll require a lot more points. We were thinking of visiting Thailand as well before heading back stateside. I'm not sure we have a specific order in mind between the destinations if that makes it easier.

We'll be flying from/to the NYC area, and I'd prefer to do this trip in business class over economy if possible. Any assistance would be greatly appreciated.