I would believe it or not, suggest Continental via EWR or IAH. I believe their Z-class fare will come in around £3000 per person, and you could get a free stopover in NYC inbound or outbound included in the price.
CO operates B767-XXXs from EWR and IAH into HNL with the same hard product as Intercontinental flights, with amended F&B service. Reviews I’ve read state that CO’s Hawaii offer is the best among US carriers. I have experienced CO on long-haul a few times, and I have been delighted by the experience.
The one drawback is that the flight via EWR is a tad long. EWR-HNL is 10:45min, so unless you plan to stay in the NYC area, I would route via IAH. On the return, it is overnight into EWR leaves around 8pm, arriving around 11am providing time in NYC if so required.