You should decide if you’re going for Silver or Gold. A vanilla LHR-Hawai’i will get at least 560 TPs in business, so there’s not much need for the holidays bonus (if available) to get Silver. Your best bet would then be LHR-DFW-HNL/OGG rtn if you can find it because it’s a lie-flat to the islands. Any ex-EU or regional start would have you over the Silver line.
If you decide to go for Gold, LHR-East Coast-West Coast-Hawai’i on a holiday would make it 1680.