Kublai needs to actually make a proper fleet instead of rushing Japan with riverboats, for one. He needed at least five years to make a fleet worthy of taking on Japan. The one he used was constructed and seized over a single year.
That said, Mongols taking over Honshu is improbable. Maybe Kyushu, but beyond that it's unlikely they can push and hold land much further. The Japanese might not have seen war in a very long time prior to the first invasion but Japan's mountains and forests make an invasion rather difficult and it being an archipelago makes suppressing revolts rather difficult (especially for a nation without naval tradition).
Also, probably want to not have the Yuan bleed out in Vietnam since that was a horrific waste of money and lives, aside from breaking the perception of Mongol invincibility.
So I'd say, to start at least, have Kublai be a bit more patient (have the Goryeo be a bit less eager for war, perhaps? The Goryeo king offering whole-hearted support and the Goryeo navy didn't help matters) and construct a seaworthy fleet (so that, even if they face opposition, the Yuan won't have their entire army and fleet sunk to the bottom of the sea). But keep him focused on Japan so that he doesn't ruin the empire by attacking Vietnam in the meantime like he did OTL. That'll help things along at least a bit.
Second invasion probably would've been a bust either way. The Japanese had a while to prepare coastal defenses and the Yuan were running out of steam due to bashing their head on Vietnam over and over.