I don't think that 2 gold provinces in Japan are not overpower.
Because Japanese embracing of institution is very slow and AI couldn't use Navy successfully, AI United Japan couldn't invade Korea and Manchu even Japan has 2 gold provinces.
And also Mutapa has 2 gold mines without price penalty. Did you see Mutapa become OP?
Japan had always run a trade deficit before modern era because Japan had many specie and there were no necessity of export goods.
2 gold mines are not inconsistent to real history.
In addition, iron was produced Harima and Aki province in Saigoku Area on Japan in history.
Still you think 2 gold mines are not balanced, change Kai province's goods. Iwami silver mine is definitely important than Kai.