Is there republicanism, or something equivalent (a monarch-less unified political entity) in chinese tradition? I mean as a political model for all or part of China itself, not only social groups or in peripherical matters.
If not, the best would be to create some sort of it, in order to avoid the "european republicanism" being simply copied/pasted.
Even before the declaration of war by the Qing court in 1900, governors of the provinces in Southeast China had discussed the ways to preserve peace in their territories, primarily against the invasion by foreign powers. Amongst them were Liu Kunyi (Viceroy of Liangjiang), Zhang Zhidong (Viceroy of Huguang) and Li Hongzhang (Viceroy of Liangguang). They had also concluded that in case Peking fell and the status of the Emperor and the Empress Dowager were unknown, Li Hongzhang would be the President of China to settle the situation.
How about this?
If the House of Aisin Gyoro was slaughtered by the Alliance, the Southern governors might be forced to try out Republicanism as a back up plan.
It's a little bit late (before 1900), and consider Li's frail health then and Yuan's prominence, the end result might be a successful Empire of China instead of a lasting republic.