I actually have an idea with this! Basically, have Sun Yat-sen and his revolutionaries instead maintain the idea of a constitutional monarchy and exploit the presence of the "Mandate of Heaven"within the culture to their advantage. After all, the Qing's Manchurian ties were a sticking point so a rallying cry would be restoring a Han Chinese to the throne descended of the Ming dynasty.
Why the Mandate of Heaven being used? Cause of this:
https://en.wikipedia.org/wiki/Mandate_of_Heaven#The_right_to_rule_and_the_right_of_rebellion
Aka, someone from the House of Zhu, preferably with leftist leanings. Even if they may not have much if any official political power, he would still be the emperor. That vast amount of cultural power and influence cannot be underestimated. He would be the representation of modern China and this who all should emulate.
And I even have a pretty good idea on who should be the new Emperor if you will.
"Zhu Jianfan (
simplified Chinese: 朱剑凡;
traditional Chinese: 朱劍凡, 1883–1932, born in
Ningxiang,
Hunan), previously named as Zhou Jia-Chun (Chinese: 周家純), was a famous revolutionary educator. He founded Zhounan Women's School (Chinese: 周南女學堂) by selling off and contributing all his property, which was valued at 111,700 silver dollars. He held the post of principal until 1927. It is a rare magnificent feat in the educational history of China. In 1911, he led students participate in
Anti-Manchurian Revolution, and persuaded
Hunan army to correspond to
Wuchang Uprising. In 1922, he invited
Mao Zedong to live on his campus, and sponsored Mao's library"
He would fit pretty well and while it may be a bit of a hard sell to convince Zhu Jianfan of it, the pragmatism of the choice and being able to put in alot of reforms would make it worth it. Sun Yat-sen meanwhile would become Grand Chancellor (in keeping the name) and thus he and his coalition could pass the reforms needing while the new Emperor would serve as a beacon of hope, the return of the rightful king if you will.