My plan would be stay up late after the DUB so get a short nights sleep prior to LAX.That would leave me sleep deprived for the LHR-LAX.Eat well then sleep for the second half of LHR-LAX,arrive at LAX go through the normal immigration etc nause then try and nap LAX-OGG.

I find the AA seats not very comfortable to difficult to sleep there.

Good luck,I bet lots of different plans will come your way.