Having done a TP run/holiday twice to the Hawaiian islands, with Mrs ST, I would definitely recommend sorting out your best option flights first. Think comfort and timings (eg LHR-LAX-HNL is doable in one very long day outbound). Note of course the HNL flights on A321s with recliners; and definitely avoid an overnight back to LAX on one of those). I liked LHR-DFW (overnight) HNL as that gets you to HNL at ~midday and you will have been able to do the immigration thing without the stress of a connecting flight.

Whatever you do you will get 560 TPs (140 UK to USA mainland + 140 to HNL). Simplest route is then LHR LAX/SEA/DFW HNL and you will be able to get BA flight numbers (so with a car/hotel) be able to double that with BAH.

If you are striving for Gold, then adding in an east coast stop will add 280TPs, potentially doubled*, but will add some oddities around timing; which may work in your favour with forced overnights. [From personal experience, avoid two overnights on planes if you can!]. *You may well be able to get BA flight numbers all the way through but doing that runs the risk of the ITA price being shot so you may just get two out of three flights on BA numbers.

Now thinking about BAH - on Oahu you will almost certainly need a car as 10 nights in Honolulu would be a waste; but don't get a car for the time you are in the city. As a result, you may find car hire for say a week the most cost effective option for doubling your TPs. An obvious comment that accommodation on the islands is eye-wateringly expensive so do see if any BAH hotel savings here make a difference.

Lastly, to echo some other comments, I would also look at visiting one other island; not only they are noticeably different, it is also a long long way to go just to see one or two 'resorts'.