What if Japan conquers Korea in 1592?

[Hansmeister]

In 1592 (and again in 1597) Hideyoshi attempted to invade and conquer Korea, but was defeated by the famous turtleships commanded by Admiral Yi. What if the invasion had succeeded and Korea had been conquered over the next decade?

There would not be an self-imposed isolation of Japan. Instead, Japan would probably seek to aggressively spread its influence into China as well as expand its naval power in the west pacific. Japan could possibly rival the great european powers in the 17th century. During the Napoleonic area Japan would take advantage of european wars by seizing the Philipines from Spain and Indonesia from the Netherlands, establishing the Asian Co-Prosperity zone 150 years early. China will have been either conquered or puppetted.

Conflict with Britain would be inevitable. How would the conflict start? How would it evolve? How would the other European powers react?