I have also just been investigating this route as I will be going there next August.
I am not sure where you are flying from but my research was limited from Singapore to Honolulu and return.
The new Scoot flights are an unavoidable consideration but for the time period I want to go, they were considerably more expensive than full service airlines.
The best option I found was actually offered via Expedia.
SIN - INC - HNL, offered via Asiana but with the first leg operated via SQ.
Return the same way, the leg INC-SIN operated by SQ.
Layover times were longer than you would wish for (4 hours going, 6 hours on the return), however, the value of Expedia was that this routing is offered via the SQ website, but was S$700 more expensive than Expedia (economy), whilst curiously the Expedia Asiana routing was not offered on the Asiana website. The Asiana website offered a routing with a layover of almost 24 hours in INC. Go figure.
And the best thing was that Expedia have a promotion offering 10x Krisflyer miles for DBS Altitude cards right now.