In the year 1263 (2960, Yin Water Pig in the Chinese calendar), reforms by Chancellor Jia Sidao in Song China began. He planned to take land from all the owner of latifundiae bigger than 1/4 sq km, which the state would pay. The surplus land was supposed to become property of the state, to make up for the needed tax money. No wonder there was much resistance, which he countered with all kinds of intrigues.
During 1268-79, there was obviously no Mongol conquest of Southern China.
Then in 1277 (2974, Yin Fire Ox), the ruler of Pagan, Narathihapate felt confident in his ability to defeat the Chinese and advanced into OTL today's provinces Guizhou / Guangxi. Although theoretically much weaker, he managed to make a lot of trouble for Song China. Rebellions of latifundia owners in the provinces complicated the situation even further.
1280 (2977, Yang Metal Dragon), Jia Sidao was toppled as chancellor and killed afterwards. The new government decided to make peace and ceded Pagan some areas along the border, to avoid paying tribute, which they could barely afford. They sent the message through all provinces that Jia Sidao's planned reforms were off - and that all those who rebelled had to be killed for their disobedience against the state, which is against Confucianism. The property of the rebels was confiscated and sold, which helped the state for some years.
Since 1300 (2997, Yang Metal Rat), Growing Nipponese piracy greatly hurt external trade of Song China.
After the Song government failed to pay the officials in some provinces in 1306 (3003, Yang Fire Horse), the unrest grew. People more and more agreed that the emperor had lost the Mandate of Heaven. In this year, the rebellions started with Szechuan seceding from the empire, becoming an independent kingdom.
In 1309 (3006, Yin Earth Chicken), all of South China was in unrest. The emperor was killed in the chaos. Jin China also used the opportunity to plunder and annex parts of the Yangtse area. Many wars and revolts shook up South China for some time. The Song dynasty had ended. Later, Hong China would take its place.