I'm up for something silly right now. With any PoD after 1185 have a European force or a descended clan establish a foreign based shogunate in Japan.
Depends on whether the British think it is a good idea to offload a rather large sum of their debts to the BEAC as part of the deal. Huge loan in the governments favour, reduction of debts, yadda yadda. Play the balance sheets so that the BEAC is stuck handling the debts. That frees up the government a bit. Plus, the Dutch continued to trade with Japan even when limited, forcing open those markets at the very least puts Britain in the position to control both trade from Europe to Asia - but trade within East Asia and the Pacific itself. With both Chinese, and Japanese markets opened, they are also open to one another - and potentially America. Lots of Pacific Trade. (Although, that pretty much means Hawaii is on top of the list of "Things Britain Wants".But would the British lend the BEIC money to conquer Japan? Because the wars in India nearly left Britain broke which lead to the Opium Wars in the first place. Japan would give them a market to sell their goods but it doesn't have the resources India has.