Hopefully knowing the flight times will be useful, but, as kcvt750 has inferred, any useful advice or opinions will depend on WHERE the band are playing. If it's in one of the cities, as you say, there may not be any need for them to adjust to local time at all.

Another question is can any of them sleep in economy seats? And how hyped are they about playing in Japan? (the adrenalin factor should help).

I spent nearly a decade putting on bands in London, often having people stay over, (it's pretty much a given you'll know a few of them) what mostly affects their ability to cope with time differences, exhaustion and jet lag is how good a time they're having.

Summers can be pretty nasty (but I guess they'll be used to that if they're coming from New York) so that will take its toll on them too.

But without knowing where they're playing, there's not much advice anyone can really give.