Re: OP. My own best luck has been in late April and early May. Though nowadays with a number of airlines flying in to OGG and KOA from the mainland and interisland prices dropping, you would seem to have more seats and better odds on some airlines, like NW.

A nice thing about early May if you're going to HNL is the Cazimero Brothers' annual May Day concert at the Waikiki Shell. Definitely go see if you get a chance.

I also don't feel very sorry for the interisland carriers like AQ and HA, as I've found them in the past to combine Hong Kong courtesy with Polynesian efficiency on the interisland routes, making the experience slow and irritating. No wonder so many people are flying to just one island at a time and staying put.