PoD must not be later than 1880
Methinks you've done a swapsey-roundey, Elfwine - the PoD must be 1880 or earlier, not later.
My suspicion is that whatever the PoD (and subsequent further divergences) is, it needs to lead to a China that is outward-focused and engages significantly in mercantile adventurism. My reading of history is that this is generally what led to European dominance in world politics, since a European country could send a force halfway across the world to tip the balance in a local dispute and thus win concessions and allies, which many European nations were later able to leverage into exerting economic control over said regions.
Question is, what does it take to have a China that does this? The trope I'm familiar with is the idea of the Southern Song focusing on overseas adventurism, in the South China Sea and beyond, in a timeline with a butterflied Mongol expansion. Perhaps the north remains fractious under squabbling princes, but strong and united enough to prevent the consolidated south from expanding back into the plains for a few centuries, long enough for mercantile interests to become strong and politically important in the Song court. Then, even when it would be later possible for the southern Song to reunite China, they continue to focus on advancing trade overseas, and in the 16th century they establish trade with European powers in the Indian Ocean, with European traders demonstrating an interest in going further eastwards for better trade deals and market expansion, but critically the Chinese traders would be going the other way, until there's a Chinese route to the Ottoman Empire. Spices and silks for guns?
As long as the expansionist/mercantile forces in China are politically powerful enough, and economically important enough, then even when China unites again, hopefully the court won't be able to become too focused on internal politics, since an outward outlook, and the maintenance of overseas trade missions, trade colonies, etc will be too financially lucrative and strategically valuable.