Why not the Saffarids?
After reuniting Persia they could take their veteran forces into India, and rule from Sistan - you just need it to survive Ya'qub's death!
I'd be tempted to suggest that if stable, and ruling from Sistan, they could go to conquer the Arabian Peninsula, but it require them becoming a significant naval power.
Regardless, if they had significant naval power, they could take advantage of the now-islamisising indian ocean, and better control their farthest Indian territories without moving their capital into the Subcontinent.
If Persian becomes the language of government over the various subcontinental languages, and (somehow) handles the religious problem - the stability, strength, and communication by sea could leave them well placed to protect themselves from potential naval interlopers. Especially if they sought to dominate the trade anyway.
Persian Zanzibar/Madagascar/Andamans?
