In terms of ex-EUs to HNL south of £2k, I sadly didn't find anything in my earlier searching - although I could've been more thorough.

For anyone interested in the Double TP fare, after quite a lot of playing I have finally made it work. JER-LHR-HEL-JFK-LAX-HNL-LAX-JFK-HEL-LHR-JER is possible for £3.8k, giving 2200 Tier Points with BAH, which I think is the most available for a single ticket in the entire programme. That's something I'm likely to pursue. At ~£1.70/TP excluding car/hotel it is on the verge of a good deal.

BA also knocked off a couple hundred quid from the Matrix fare when I called to check a similar routing, so I am hoping the above figure will be reduced when I go to book it.