Where there is a will, there is a way.
Once again this argument comes simply back to thinking people can do much and thinking people can only do too little. Despite the fact that human history has literally moved mountains on more or less.
Though, really. What was the motivation for Columbus then to prove he was right and reap the awards?
For Japan it would have to be "OK, we know that somewhere to the East some barbarians conquered even more barbaric, barbarians who found Mountains of Gold! Reason states that if there is that much around then there must be more! If they could do it, then so could we."
Perhaps then the involvement of Japan in the Americas would not be out of sheer minded will of the State, but pulled on by rising needs and desires of persons and to counter rivals. Such as what happened between the English and French. What would a Japan that is non-isolationist, but not interested in invading China or Korea do? As the Manchu cut themselves off from the world the Japanese would be interested in filling the vacuum left behind and become quite energetic. Establishing trade posts on the peripherary north of Manchuria to trade with the locals for horses, lumber, establish iron mines and so forth-creeping north and eastward into Alaska as traders, fishermen, and whoever else get pulled into the region as it develops through state and non-state actors.
Japanese merchants and workers lured by gold and opportunity travel to New Spain and set up roots and decide to branch out. Perhaps the Japanese decide to find the Northwest passage or some European arrives in Japan to do that by recruiting resources locally. Maybe they get into a fight with Spain, and someone comes up with the idea to counter the Spanish by threatening their position in the New World.
Should be VERY hard to see "an expedition into the unknown" as the same as "an expedition that promises a shorter voyage to a place we already know".
They really did think he would die or fail.
