Then again, there are descendents from the Ming and Song families, or at least the Tang, right?
Yes, except we wouldn't know. Many descendants of a previous dynasty would change their surnames in order to escape from purging of the succeeding government. Besides, Ming carried the surname Zhu, Song carried the surname Zhao, and Tang carried the surname Li. Those are very common surnames in China, it's hard to identify. On contrary, Qing monarchs were left alone because when Emperor Pu Yi abdicated, he and his empress dowager Longyu, signed a contract with the government of Republic of China, which guaranteed to continue to let the Qing monarchs reside in the imperial palace and would receive regular salary. Also, because Qing monarchs were Manchu, they had an unique surname (which is Aixinjueluo), so they're easier to be identified.
In fact, I know a descedant of Qing is now a model in Hong Kong. That princess is quite hot indeed.