The Russian expansion to the East is stronger than OTL, instead of staying north to avoid confrontation, Imperial Russia spreads forth in every direction.
As result, the Russo-Manchu border conflicts start earlier, and are more ferocious. The
Treaty of Nerchinsk is never signed, and Russia maintains hopes of conquering China.
In around 1640, the Russians advance on Shengjing and depose the Qing emperor. The Russian Tsar usurps the position of Chinese emperor, just as many invading forces had done before him.
This sees the start of a prosperous Russo-Chinese personal union, a new border is drawn up, one that strongly favours Russian advances into northern and western China - meanwhile, the Chinese Empire concentrates on expanding southwards. The capital is moved to Nanjing, and Tibet, Burma, and parts of Indochina. At about the same time, England has started to move into the Bay of Bengal...
For much of the 1700s, English India and Russian China, (while the English are running India quite directly through their corporations, China is still pretty much run by Chinese, the Emperor is a white man sat in Moscow, but his court is staffed two-to-one by native Chinese, and aside from a few European experts, the civil service and the merchant classes are Chinese), compete within the Bay of Bengal. There is a fairly clearly defined border between the two, zig-zagging due north from a point roughly half-way in the middle of OTL Bangladesh.
In 1846, Russia falls to a liberal republican revolution. The Tsar flees to Nanjing, but many of his immediate family chose instead to seek asylum in other European capitals, especially London and Paris. The situation in Nanjing is tense, everyone fears a Russian invasion, (the Chinese, at this point, have almost no independent military force to rely upon). While Northern China prepares for war, Southern China is neglected, the previously well-administered rule of law begins to evaporate and piracy begins to take hold in Canton and Indochina. Meanwhile, on the other side of the peninsula, the Burmese (among others) are taking the oppurtunity to fight for their independence. England, meanwhile, is sweeping up all the East Indian profits.
At around the same time, the first born daughter of the aging Chinese Emperor falls in love with the young heir to the English throne. And shortly thereafter, the first born son of the aging Chinese Emperor gets himself killed in an opiate-fueled scrap in an underground Parisian social club.
In 1852, the English king is assassinated by a deranged republican. His young heir and his Russian wife ascend to the throne. In 1855, the Chinese Emperor finally dies. The major powers of Europe assemble to discuss what to do vis a vis China, there are three options on the table: do nothing and let the Chinese handle themselves, (this is unfavoured as many point to the bizarre and dangerous social movements arising in China), follow the letter of Russian salic law and hand the Chinese throne to the deceased Emperor's oldest surviving son, (this is unfavoured because the Emperor's oldest surviving son is considered a nincompoop and a deviant), or, hand the Chinese throne to the King of England, whose claim through his wife, is, arguably, the strongest. The great powers decide on the latter option, mostly because they feel that the economically liberal, free trade-orientated English will be able to stabilise the Sino-Bengali traderoutes.
The English do not disappoint. The copy the system they have been using in India and send a governor to Nanjing, along with a considerable army presence. Shortly thereafter, they grant independence to the Burmese, (most of the Burmese... the highlands are maintained, but, in return, the Burmese are given control over much of OTL Siam, which, in TTL, didn't manage to so skillfully maintain its sovereignty). Indeed, the English do much to downsize China, rebellious nationalities are given their independence, and the lords of unprofitable provinces are given much more independence, essentially becoming Chinese Princely States. The remaining British China is a patchwork of governorates stretching from the coast to the Bay of Bengal.
Over the next century, the two hostage nations advance significantly. Railroads are established to help extract resources more efficiently, and, as the populations become more educated, increasingly complex industries are established, the patchwork pattern of direct control and vassalage has expanded hugely, stretching outwards from the core territory of East India and South China, all the way, uninterrupted, to Central Asia.
(This, of course, doesn't last untill the end of the 20th Century...)