As others said, not many great options to get United flights using Amex. If you're open to other routes (again, not sure what route you're specifically looking at) there seems to be plenty of options to get to the mainland in business by transferring to Qantas (flying on AA, such as HNL-->LAX on 2/12), transferring to JetBlue (typically flying on Hawaiian, such as 2/12 HNL--> SFO), or Delta (a lot to SEA, some to LAX).

Traveling to the East Coast may be tougher but still doable. If you let me know where you're heading I can give more specific advice).