As mentioned in other threads, I always do and recommend printing and bringing with you a copy of TSA's policy and the particular airline's policy.
I've had gate agents spew all sorts of things that wasn't on either policy. Handing them the copy of the policy helped refresh their memory of THEIR OWN policy. One gate agent was insistent that the locks on my rifle case needed to be TSA locks and was going to reject my rifle case. I would do that even if I confirmed via email, call, etc to the airline.
I usually get to the airport early anyways, but the 20 minute extra is a good tip, particularly for HNL. Some airports have you take your rifle/gun case to a TSA screening area where they swab, scan, etc the case and then either accept the case or ask you to open it up for inspection.
Also be wary of the gun laws in states where you have a stop over. This could be important if you miss your connection and the airline may ask you to claim your luggage.