The POD in "Superpower Empire" is in 1912, so it doesn't meet the challenge's requirement. In fact, the reason I chose that date in the first place, was because those attempts at imperial restoration that took place later on in OTL ended in failure. I consider that 1912 was the very latest date when such a restoration could be successfully carried out, at least in order for things to turn out as well as they do in my TL. One reason for that, after 1913 and Yuan's replacement of civilian provincial governors by his cronies from the Beiyang Army, descent into warlordism was practically inevitable; another was that, in spite of Yuan's shenanigans, the politically involved Chinese elites grew to consider the Republic the most appropriate type of regime for China, and going against that consensus would have taken uncommon skill and charisma.
In OTL, apart from Yuan Shikai's unsuccessful bid of emperorhood, there was also an attempt by warlord Zhang Xun in 1917 to restore the Qing dynasty.
I had just learned about him the other day. That was the inspiration for this thread. The only thing is, I don't think he had any sons. Wiki mentions a daughter whom he tried to marry to Pu Yi, but it doesn't seem likely that she could actually take the throne in her father's place.
Oh, Yuan had a plentiful descendence thanks to his many wives and concubines. His eldest son and prospective successor, Yuan Keding, was born in 1878. Incidentally, one of his grandchildren is an American geologist.