If i remember correctly, the beating heart of Nestorianism was in Mesopotamia; you need to prevent it from being conquered and, instead, form the nexus of an empire for a few centuries (or at least its heart of power).
Perhaps some situation where the Persians advance into most of Arabia (instead of just having vassal states), where most contact done with Persia proper is through Arabia, letting instead the Nestorian faith and missionaries seep throughout Arabia and become the religion of choice. While it doesn't become large in Persia, it does slowly become the religion of the wealthier class of merchants and nobles who work through Mesopotamia. So, discounting the Mongols (as the political situation will determine what they convert to, if anything), you would have Nestorianism being strong in its core in Mesopotamia/parts of Arabia, and having a strong minority in Persia.
To really get this, you need a pre-Islam PoD, probably. Mesopotamia is in a poor defensive position, and cannot weather being the wedge between three separate civilizations.
Maybe if Arabia is contained for centuries, the Arabs might convert to another religion (in piecemeal), but it might be towards one of the stronger ones.