I previously ticketed one DONE5 with QF that included LHR-HNL-LAX Also BA accepted the routing. AA didn't accepted the routing, but they promised to honour the ticket if another ow airline would ticket the itinerary. But AA said that they would not touch such ticket, if any modifications would needed.
I guess airlines that use Amadeus accept it more easily as Amadeus displays it as a one segment versus Sabre that displays LHR-LAX and LAX-HNL separately even with same flight number.

Booking HNL-LHR in A would have definitely been possible before AA recoded domestic A to D, but it's bit harder.

It might be worth booking as a DONEx and using CX, BA, AA miles to upgrade to F on flights with a true F cabin. I upgrade DONEx AA flights this way all the time. A few years ago I upgraded a CX DONEx flight using AsiaMiles. Also a few years ago, I tried to upgrade a BA DONEx flight but BA said it wasn't permitted on RTW fares, not sure if that was accurate or if it's still the case.

If you start from one of the lower cost places and value miles at around 2 cents each then an AONE is actually often cheaper then a DONE considering the cost of upgrading (and the uncertainty of finding space).
My strategy is to use AONE (or FRWSTAR) to build up mileage, then use the miles for award tickets in between.