I've voted 1 month, not necessarily because I don't believe the job is legitimate, but because Adam absolutely cannot be trusted to complete the requisite planning to get himself situated.
He is a fail son that believes applying for a visa is the same as acquiring one. He still has 0 permanent accomodation and even plans to somehow supplement his income in a timezone far, far away and hope it won't have some catastrophic effect on his tax burdens (remember, he asked if moving to Japan permanently would magically mean all US debts are expunged). Until then, he's relying entirely on extremely tenuous "promises" made by people who have been put under pressure to house him. Any polite nodding will be considered permission for Adam to show up on your doorstep.
In terms of apartment hunting, even with the help of some well-meaning friend, as soon as the landlord gets wind that the name on the lease is going to be some stinky gaijin who can bail on their debts at a moment's notice, most applications will fall through.
Also, anybody who has ever attempted long-term international travel knows that even when the grounds on which you're applying for something are legitimate, it could still take fucking ages for an application to clear. That's before we even get into the legitimacy of this job.
If he doesn't wind up living in a manga cafe on a completely inappropriate visa type or just getting arrested/deported somewhere along the line for being a gross, groomer retard, I'll be astonished.