That's interesting that Britain has military superiority versus you. They just can't compete with your factories.
I propose that you contrive some sort of WWI, even if it means loading up as the various powers, creating alliances, and declaring wars to make it happen. It's 1914. It's really time.
Britain on one side. Japan on the other.
It gives Russia, Prussia, the USA, France, and Italy, and Spain some tough choices. I would say Spain would stay neutral. Italy is still missing some Italian property but would Austria give them an excuse to go to war?
The USA would have a difficult choice between democratic Japan and the old home country Britain, but full citizenship Japan might be a tempting ally even though it threatens US interests in two areas.
So let's presume that Europe is less concerned with Japanese interests and more concerned with Prussia, which has barely failed to unify Germany on account of some shenanigans. Let us then posit Prussia deciding to force terms on Bavaria, with France objecting. Austria may object too, seeing one last chance to assert itself. That starts with France and Austria versus Prussia and Italy.
Britain would side with France and Austria in that matter. Hungary may join with Prussia.
That leaves Japan, Spain, the USA and Russia. I would say that the USA and Spain would probably wind up on whatever side Japan is not on, and Japan has a huge animosity to Britain, so Japan joins Prussia. The USA and Spain (due to Cuba) ally with Britain and France.
Russia may not have a reason to join the war at all, and may just be grateful to have avoided revolution. I would say Russia, Egypt (!), and the Ottomans would join sides based on who joined what side first.
So the great war over Bavaria! Britain, France, Austria, USA, Spain versus Prussia, Japan, Italy, and Hungary.
Just make sure to impose some collapsing peace on whoever loses. That'd require more editing and releasing of states.