I do this flight quite regularly. Can I suggest the Virgin Atlantic or BA
flights to Los Angeles and then Hawaiian. As they say here it's a short hop across to Hawaii from west coast usually not much more than 5 hours (slightly less from San Fran - bu worse connections) and then connec across in First on Hawaiian. It's a comfy arm chair, but
On the a330 you have some great entertainment options and the foo really is first class.
As for body clock get about 3 hours sleep on the LHR
flight and you'll be fine as usually you arrive early late evening which means you'll be tired enough to get a decent enough sleep. As virgin and Hawaiian are partners they can book the whole thing for you and they depart from the same terminal at LAX
too, which is V handy. They have decent return connections too.
Don't worry about body clock, really.. It's a long... but not painful trip. Feel free to email me if you want more info..,