Eg, Feb 19 HNL-NRT, Feb 23 NRT-TPE. It's out close to the end of the schedule though. I didn't realize that award space from HNL was so tight (I guess it makes sense since so many Japanese people like to go to Hawaii on vacation... probably this is their own members using up all the saver award space)
Leaving from SFO, LAX, or SEA might be "easier", if you consider a 5 hour repositioning flight easy...
Edit: I was totally wrong about the married segment logic. What I thought was business space when you added the connection was actually just mixed space, as you pointed out. But the TL;DR here is that you probably need to either leave from from somewhere other than HNL, or book right out at the end of the schedule.