The direction that Paradox has taken (due to only having a single Emperor of China at the time) is to skip South Song.
This means that Song reign ends in 1127 when they're conquered by Jin (whom they actually survived) who are later conquered by the Mongols 1234.
As both Song and Jin are "gone" by 1234 they install the Genghis Khans successor as Chinese Emperors instead:
- Ogödäi Khan (1234-1241)
- Güyük Khan (1241-1248)
- Möngkä Khan (1248-1260)
- Kublai Khan (1260-1294)
Meanwhile, they leave on map Mongolia in the hands of placeholder characters.
Their choice is understandable, but I disagree with it entirely. In my opinion, the line of Taizu should be added and South Song Emperors should be added to the history files. Whether Jin should be considered rulers of China after 1127 or if Song can continue to rule with a Jurchen invasion status between 1127 and 1211 (where it's replaced with a Mongol Invasion) matters little, although I suppose adding Jin feels a bit more varied. However, after the fall of Jin in 1234, South Song should be considered rulers of China until the rise of Kublai Khan. This means that Emperor Lizong rules from 1234 (or 1224 if Jin aren't included) until 1264 when Emperor Duzong takes over before being prematurely ousted by Kublai in 1271 (or could possibly be allowed to rule until 1274, and even toss in the last few emperors until 1279, letting Kublai establish the Yuan a few years late).
Also, in 1260 the game splits Mongolia off from the Yuan control. But I don't think that is historically correct.
When Möngkä Khan died in 1259, both Ariq Bögä and Kublai laid claim to the Mongol Empire. As the youngest brother, Ariq Bögä ruled the heartlands of Mongolia and summoned a Quriltai to get himself elected khan. But Kublai was away from court (campaigning against South Song) and kept avoiding Karakorum so as to not lend Ariq Bögä any legitimacy. Instead, Kublai gathered an army to oust Ariq Bögä and was proclaimed khan by his supporters (I'm not sure who they were exactly as most of the Mongol nobility supporter Ariq Bögä) in 1260. A war was fought between Ariq Bögä and Kublai called the Tolouid Civil War and lasted until 1264 when Kublai won.
In my opinion, the perfect mix of accuracy and gameplay consistency is to mark 1264 as the year of Kublai's ascension to the throne of China. This allows Kublai to be a landless pretender to the Mongol Empire while Ariq Bögä is in charge (meaning he can become an adventurer or have his claim pressed by Hulägu or whomever) and become Emperor after his younger brother is defeated. 1264 also coincides very well with the death of Duzong (only 2 months between the defeat of Ariq Bögä and Duzong's death) meaning a smooth transition in the history files. Also, by 1260 Kublai had already made Khanbaliq (Beijing) his capital and never moved back to Karakorum so being entirely off map is fitting.
After Ariq Bögä's defeat the Mongol Empire is disbanded (the suzerainty of the successor states is transferred to the Western Protectorate, i.e. Yuan Empire) but the region itself is controlled by Qaidu, Ogödäi's grandson and Kublai Khans later (and much more dangerous) contender for the following 30 years. Qaidu eventually become de facto ruler of the Chagatai ulus which is probably best represented as a tributary relationship. After Qaidu's death in 1301 his son Chäpär lacked the strength to keep up the struggle and accepted Yuan suzerainty, he was later defeated by his Chagataid appointee Duwa and was forced to relinquish all control over the Chagatai ulus. Later, after Duwa's death, he tried to reassert the Ogödäid ulus but was soundly defeated by Duwa's son Kebek and fled all the way to the Yuan court in China. Whether Mongolia should be a part of the Protector General's realm (as Tribal vassals) or part of the Chagatai ulus after Chäpär's defeat I'm not sure, but regardless it should stay that way until the end of the game.
I wrote about this about a year ago if you're interested. I no longer stand by all I've written there (and a lot of it is probably just a repetition of what's written above) but some of it might be relevant.
