When you call to talk to the airlines, don’t settle for the first answer you get, especially if it isn’t the answer you’re looking for. Some agents on the phone just aren’t as skilled as others in finding what you need, so call back and speak to someone different. If necessary, keep doing this until you get what you need. This is especially true for airlines, but this can work with hotels and car rental agencies too.
For example, we tried to book our flight to Sydney through United, but were told that no award seats were available because we were booking them so late. After two more phone calls, we got someone who looked at all the partner airlines and found two seats leaving from Vancouver on Air Canada, a partner airline. It cost the same award miles and wasn’t as convenient as flying out of Seattle, but the benefit was that we now have a direct flight with no layovers.