Not saying that something as fast as what Japan did is possible.
However, that's not necessary. All that's necessary is to modernize to the point that they could (for example) beat back the French flotilla in the Sino-French War, and hold Taiwan against the Japanese in the 1st Sino-Japanese War. They fought off the French
land forces, and their navy was modernizing, so that's definitely possible. In fact, if the Fujian Fleet hadn't been left to fight Admiral Courbet's forces alone by the other three fleets, they still had the possibility of winning.
And if reform efforts had started a good 10 years earlier and not been severely restricted by a hostile imperial court (ie. Cixi), that could
easily have been done. They built Western-style shipyards and arms factories IOTL despite all the meddling, so a reform effort that isn't retarded by Cixi's meddling would build even more and would at least
attempt to keep up with Western advances.
Why would greater British success in European wars make it more likely for them to succeed in diplomacy with the Qing in the 1790s?
That requires them to first not fuck up Qing diplomatic procedures and then to lay out something persuasive about the benefits of trade.
If anything, an earlier war with the Qing might actually shake them into a modernizing mindset before the economic and bureaucratic problems of the empire really
start to fuck it up. There were already a few people warning about how China needed to modernize its military to keep up with Western powers, even in Qianlong's time, and British victory in war would give credence to their concerns.
Why would a Han dynasty be less likely to be gripped by reactionaries than a non-Han one?