If they are willing to use an obscure online travel agent, try searching on skyscanner (and use one at their own risk). My quick search showed $5003 as the cheapest for a round trip of JFK-HND direct operated by JAL. AMEX IAP is offering the same for $5448 but this requires AMEX Platinum (or higher) membership. $5.9k for NYC-TYO is actually pretty good deal considering there used to be much wider price gaps in business class prices between west coast & east coast until recently.