Since this issues is soooo complicated, I'll be helpful and volunteer to go with you to Hawaii if you'll just pick up the airfare.
I'll handle all the weapons through security... Both ways.
Seriously....
Looking at your photo from the OP, if those side clips can be opened and the case cracked without opening the lock, that case is likely to be rejected by the airline and tsa.... You need a case that cannot easily be pried open AT ALL.
Nanovault is $20 at Academy and comes with a cable that I wrap around the metal bits inside my wheeled luggage. Even if they open the cheesy TSA lock on the outside of the bag, they'll need to steal the whole bag to get the gun.