I don't understand why there's all this focus on the "illegal connection" business - that was fixed before the travel - the actual flights that OP was trying to check-in to at Miami were, apparently, MIA-ORD-NRT-MEL, presumably on AA then JAL for the next two segments (since as noted, QF doesn't fly NRT-MEL). This involved no entry to Japan except for the fact that for some reason AA wasn't able to check the bags all the way to MEL. To me the root cause of the problem lies in this part of the story:
Was this really correct that JAL would not allow the passengers to board? I think not, we have seen many other cases where transit at NRT was allowed in similar situations even when tourists could not enter the country. So unless the OP is deliberately obfuscating the story by telling porkies about NRT vs HND after the first rescheduling, I tend to think that they overreacted in the stress of the situation by assuming that they couldn't travel through NRT, without properly checking, and then demanding the alternate routing. OP made the whole situation much harder for themselves by not at least proceeding to ORD where JAL staff, who would be much more knowledgeable about the situation, might have sorted out the luggage issue.