I purchase First Class tickets on the JFK / HNL / JFK flight for this June.
At the time it was not possible to book the connecting Interisland flight -- IT problems at HA.
I finally got around to booking the Interisland --- the fares are outrageous.
I travel at 3 times a year --- and I have never seen fares this high ---
for 2 round-trip tickets HNL / LIH it is just under $600.00 (in coach).

Obviously HA doesn't miss Aloha Airlines. ( I do -- pricing reasons only).

Cheers!!!!!