So, it seems that thus far the possible solutions are surrounding Safavid Persia and Fatimid Egypt (reasonable, given that they were probably the most powerful pre-modern Shia states).
For Fatimid Egypt, it seems as though they never got very far in converting their own people, and their position in the world is at least somewhat limiting as well, because the bulk of the world's Islamic population is further east, and the competition in the areas that they could concievably influence (North Africa, Arabia, the Levant, and possibly Anatolia) is very stiff.
So what about the Safavids? They were far more agressive and successful in proselytizing, both in their own territory and beyond their borders, and they are better positioned to influence the massive Muslim populations in southern Asia. Still, their agressive style meant that they could only proselytize about as far as they could project their military, which means that their maximum range is probably Pakistan and Northern India, and the latter only with a greatly reduced Ottoman threat.
To help with this problem of military proselytization, is there any way that the Safavids could have centralized Islam into a more stable heirarchy (based loosely on the Catholic or Orthodox model) and used this as a base for sending out missionaries to areas otherwise beyond their reach? Persia did have a highly influential culture, so missionaries would have the benefit of coming from such a prestigious background, which might help in less developed areas especially, though that probably wouldn't help too much in the Arab world.
Another possibility I'm curious about is that of Shia Islam becoming a sort of cultural response to the Ottomans, who were obviously not descendants of Muhammad, but still claimed the title of Caliph. If resistance to their claim is strong enough, do you think we could see more Islamic countries, not wanting to see a new Caliph with de facto power, begin to adopt a stance that favors only blood relations of the prophet being eligible for the caliph position, and thus leaning Shia?