I have done UA/NH itineraries more times than I care to remember and have the following experience (UA-NH-UA connections only).
- departing from U.S. on a UA flight and then connect to NH (whether the connecting airport is in the U.S. or in Japan is irrelevant), it is three bags for those M+ members with the appropriate status.
- Between US and Asia, and NH as the first carrier, if the ticket is issued by United ( not NH or other carriers), NH will honor the three bags allowances for those with appropriate Mileage Plus status.
- on RTW tickets issued by UA (016 stock), same as above on flights between US and Asia.
- on RTW tickets issued by other *A carrier, if the first flight is on NH, then it will be subject to NH baggage allowance based on cabin of service + *G additional allowance.
YMMV.