It isn't impossible but you usually need to fly midweek. In the last 4 years I've non-rev'd about 6 times to the islands from either SFO or LAX, nearly always leaving on a Wed. I check the loads frequently on United, and they are "nearly" always full outbound Friday and Saturday.

I've also been at SFO waiting to fly NRSA to Kauai and the planes filled up. No trip.

Lastly, you are trying to fly right when most US schools are ending their year and 2 airlines flying to/from the islands went "tits" up. Less capacity means less seats available.

Just for kicks I checked SFO and LAX to KOA loads leaving this Fri (5/2) Sat and Sun. Chances are not good of getting on any of the 3 flights. I also checked 6/20-6/22. One flight is already completely full and the others are getting pretty full. If they are pretty full now they will probably be completely full when 6/20 rolls around.

Your mileage may very though.