Sinicization is probably overrated as an answer - even the Manchus didn't fully 'Sinicize'. As mentioned, the process generates trouble of its own with Reformist/Old Guard conflict (as the Northern Wei found out in the 7th Century when their entire Old Guard revolted away), so here's my list of alternative solutions:
1) Get rid of the practice of distributing loot to Mongol elites every time a new Emperor ascends to power. A pretty common feature in the 'tribe-state' system of steppe politics, it nevertheless became a massive burden after the Yuan reached the limits of its expansion and began extracting higher and higher taxes to sustain these payouts. The turbulence of Mongol politics mainly stemmed from Emperors failing to match/increase previous payouts... a strong Emperor could engineer an Ottoman-style 'Auspicious Incident' to enforce his authority on these matters.
2) Better choice in wars. Kublai engaged in a frenzy of expansion at the same time as and after the Song conquest, which exhausted the state's resources (especially precious maritime resources, which are not easily replaced) without bringing much profit in return. A more focused approach on specific targets (Annam, Japan, Champa, Java etc.) could have yielded tangible results that, in turn, could have provided loot to pay off Mongol elites and thus keep the realm stable.
3) Allow Chinese access to the higher echelons of power, similar to the Manchu system. The fact that Han Chinese found themselves trapped into low, provincial posts did not do much to help bolster their loyalty to the Yuan state. Of course one could very well argue that attachment to the Song was extraordinarily strong during this period and that Han wouldn't have served in the Yuan state even if they had been allowed to anyway, but the fact that the option wasn't even there didn't help things.
4) Lastly, put fewer Tibetan lamas with little administrative experience in positions of power.
It's more difficult to sustain a Yuan Dynasty than the OTL Qing Dynasty, since in the latter's case the Manchus had done away with the practice of loot distribution and Han Chinese proved far more accepting of their rule than they were of the Mongols during the Song period. However, the Yuan also had advantages in their societal openness, as well as the existence of commerce-based 'strongmen' across the former Song Dynasty (such as the Arab Pu Shougeng in Quanzhou) who could be used to hold down the fort.