The map seems accurate.
It seems, however, that Yamato expension went westwards : is there a connexion with these centers being closer to Korea and from trade ways?
It is likely that Yamato sought to secure hegemony over the richer west and become the preeminent Kofun state before marshalling its new power against the north.
What makes it logistically "inevitable"? How about having a power centre in northern Kyushu and another in Yamato, such that for a period of some centuries neither is capable of subjugating the other? And this situation might come about even after a previous unification, as a result of a civil war ending in a draw and partition of Inland Sea...
Inevitable might be too strong a word, but I do think the area around the Inland Sea will at least be economically integrated even if it isn't politically unified. That said, the prospect of a western and eastern state that consolidate and grow in opposite directions for a few centuries (like Silla and Goguryeo) is also plausible and also quite interesting.
I suppose that in such a scenario, the western state would likely include Kyushu and Izumo (Kibi, which is mentioned as being a rather martial society, may serve as a buffer between it and Yamato) and have a capital around the area of
Dazaifu.
Meanwhile, Yamato might develop along the lines of the Warring States Qin-- cut off from easy trade, it instead launches piecemeal campaigns against the Emishi to seize and develop agricultural land and increase its fighting-age population. I can see it inching along the Tokaido to present Tokyo Bay. If a confrontation with the western state were to occur, it would likely contest control of Izumo or Shikoku.
EDIT: If the two states remain separate for long enough, I can see religious differences accumulating in their societies. Kyushu would likely be the first point of contact for Buddhism, and with its connections to Korea and China it may end up adopting Buddhism fairly quickly. But what about the eastern state? Might it cling a little closer to the precursors of Shinto, seeking to differentiate itself from its rival?