HNL-mainland is the hard part. From there, cheapest option would be DL, AF, or KL with KE miles (80K roundtrip), but getting the mainland leg will be tricky unless you just bite the bullet and buy it, and KE has a reputation for being a bit challenging to deal with by phone. Beyond that, lots of options through UA, BA (with fuel surcharges), and now AF/KLM.

I haven't seen any recent reports of UA bookings via Asia, but if they'll still do it, you'll find wide-open availability to ICN on OZ and multiple options from there, plus spottier availability HNL-TYO and onward. It's a little farther that way, and definitely not bookable online, but you'd be doing the community a service if you'd test whether UA will let you book those routings and report back! 70K for one-stop service to most of Europe would be pretty sweet if it works.