I know there's a ton of context around the Japanese surrendering to the US because they were afraid of Soviet reprimand (I think), and worried about Communist thought in the country (I presume, at least). But if the fighting would have gone to the bitter end, with both the Soviets and Americans having to launch naval invasions of the Japanese mainland, were there any plans in place with how to deal with it? Would they divide it up, like Germany, have a "race-to-Berlin" style land-grab to Tokyo, or merely just let the other faction focus on it because they did not want to deal with the issues that could surrounding occupying Japan?
They didn't work anything out ahead of time, if that's what you're asking. The US "full scale, dragged out" invasion plan involved a full US invasion of Kyushu and Honshu. It did not incorporate a Soviet invasion. If the Soviets had, say, invaded Hokkaido, if Europe (or even Korea) was any indication, that would have affected the postwar "split" quite a bit — "boot on the ground" determined postwar power allocations arguably more than anything else.
It is of note that while aspects of the European split were considered before V-E day, most of the permanent decisions were made at Potsdam, and were reflections in part of where the Allies were and weren't.