Agree re flying outbound via ORD/DFW -- the 763 LAX-HNL is early in the morning. On the return, though, you may want to consider the 763 HNL-LAX with the connection LAX-JFK, esp. if your award is in F/J and you'll have the 762 J sleeper for your redeye return.
I had no trouble getting 5 award seats in F/J on the same flight LAX-HNL in June. Maybe that's why you can't get any? Sorry!