AHC/WI Shia Ottoman empire, sunni Persia based empire?

Have the the ottomans (or another anatolian turk dynasty) create a shia empire based around Istanbul, and sunni empire that like the Safavids gets their empire recognized as a continuation or Iran imperial tradition.
 
A simple way for Shia to become the religion of an Ottomon state may be via the Janissaries and the Bektashi Order. Have the syncretic and partly Shia inspired practices of the Bektashi become more deeply rooted in Shia and more heavily influence, even convert, a majority of the Janissary corp. With the right inattentive Sultan, the Janissaries become a sufficient political threat to enact a coup and impose their new religious oractices on the court and then the empire.
 
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