The original plan was to buy economy-class tickets, upgrade to business class with miles, and stop over in Singapore on the way. That plan fell through when it turned out that Singapore's in a different "region" and the stopover would turn the trip into three separate legs. Then it turned out that upgradeable economy class tickets were insanely expensive (not as bad as business class, but more than twice the non-upgradeable fare). But it was possible to buy enough miles to obtain business-class tickets outright. Also, looking at the itineraries of the Star Alliance partners we thought we'd be able to stop over in New Zealand on the way. But that too proved infeasible -- New Zealand Air is extremely stingy in releasing business-class tickets to its partners.
So here's what we wound up with: we'll be flying business class PDX-LAX-SYD-MEL, departing on August 25 and returning on September 22. The Worldcon is in Melbourne September 2-6 and our itinerary is otherwise completely open.
Business class makes a HUGE difference on a flight this long. Because of the arbitrariness of upgrade awards I was really worried we wouldn't be able to get it, so I'm greatly relieved. The additional miles we had to buy to make this possible cost a little more than one economy-class ticket, so we're flying business class for about half the price of economy (plus, of course, every single mile in both our accounts).
Now that we've reduced our United mileage balance to near zero, I'm seriously considering switching to Alaska as my primary mileage account. United does fly everywhere but it's sometimes been extremely unpleasant to deal with them.