The AS booking system is buggy. It has been for years. They don't care to fix it unless it is an under pricing bug. They may fix one bug and cause another. It's a mess. Calling the partner desk and getting a competent agent can usually help.

The online system currently has a problem booking mixed cabin through TYO (maybe others, who knows?). I did some checking and found I could make an online connecting mixed cabin booking without a stopover in TYO but their system only shows mixed cabin itineraries that connect at the same airport (HND or NRT but no mixing). HND and NRT are co-terminals so you should be able to mix them with a stopover by calling the partner desk and feeding them the specific flight numbers, dates, and cabin classes.

Have you tried searching for TSA instead of TPE? JAL changes up the schedule from time to time but currently it looks like flights go either NRT-TPE or HND-TSA. This may cause additional heartburn when trying to mix a HNL-HND with a NRT-TPE since the connecting airport is not identical. It does not have to be in this case since NRT and HND are co-terminals but the AS online system will not show it (and because of another bug they won't even show through the same connecting airport when asking for stopover). Calling the partner desk should be able to solve most of this so long as you get a competent agent. Make sure to call on the partner desk number, AS business hours are recommended. It is common to have to call back more than once to get a competent agent.

There was another bug where the system (both online and the standard agent system) would not price a stopover longer than 14 days. I don't know if this is still an issue.