Sorry about the late response:
dooley - I think your original itinerary was more than an open jaw - since you wanted to end up in a different city from where you started - I think the alternative you came up with works best open jaw starting/ending in ATL - and just buy a one way ticket to NYC afterwards.
Diane - Delta has gotten very stingy with "low" priced award tickets especially in Business class - they're actually more likely to release the "cheap" seats closer to departure than when the schedule is loaded at 331 days. You would be limited to Delta with your Midwest Express miles (it will at least have to be Delta codeshares - and not simply a partner).
Olivia - I think you've also run into the problem with US instituting a 3-tier award structure which started on 1/14/10.
Kathy - Air NZ is Star Alliance so would partner up with United / USAirways but their Business Class award is probably the hardest award to get anywhere. Qantas is oneworld and partners with American. Virgin is pretty much independent. My suggestion for you to use DL miles would be to do a RT award to SYD from LAX and just buy the one-way AKL back to SYD to catch the flight back to LAX - going through ICN makes little sense.