I'm not sure JFK-LAX-HNL-LHR works as the rules state you can't back track to CONUS. That means you have have to do US-Hawaii-Japan or US-Hawaii-Australia or vice versa. I don't believe the HNL-LHR will work, but would love to be proved wrong.

Also, you aren't using many F class flights. I would consider getting a DONE and using the savings for a couple bottles of champagne on the ground.