Japan's strategic dependence on an Anglo-American partner

Could Japan remain independent of both Britain and the United States and still win a major naval war?

No; Japan could hope to fight one only when the other was distracted, and ultimately needed one of them as a partner.

The Japanese war plan became viable only after Britain was deeply committed in Europe. Japan might hope to defeat one great naval power while the other was distracted, but facing both together was beyond its capacity. A conflict with either Britain or the United States would tend to pull the other Anglo power in, because neither wanted its partner or rival to emerge with uncontested Pacific influence. Japan therefore faced a two-power strategic trap and needed alliance or accommodation with one of them.