As others have said, this will be very difficult as competition is intense for very limited supply in peak season.
In reality, your family (and you!) need to make a decision: direct in Econ or Premium Econ or (very) indirect in Biz. If they do accept the latter, look for all OW exit points (miles or paid tickets) from Japan: Sapporo, NRT/HND, Nagoya, Osaka, Fukuoka, Okinawa, etc… Some of these are seasonal; it’s probably not a full list. I’ve used BKK, SIN and HKG as transit points to connect to OW miles tickets for long haul to Europe. You can also add KUL to your search. You’re probably looking at total travel time of >24hrs if you choose indirect.
If your exit from Japan is on JAL, they’ll thru-check luggage to your final OW destination which makes it slightly easier as you’ll avoid immigration and the need to recheck at intermediate points.