Well, it's fairly easy to take out the Moghuls with a 1500 POD: Babur was still the ruler of a fairly dinky kingdom outside of India/Pakistan proper. One problem is that the Safavids come to power in 1501: if you get rid of them either you have a fresh period of fragmentation and unrest or perhaps even an Ottoman conquest: if you keep them, you have the problem of resistance by mostly Sunni neighbors to the imposition of a millenial Shi'a regime.
Another problem with the idea of an "extended Persian cultural sphere" was that there already was one - Persian, after all, was the court language of the Delhi sultanate, and in turn of the Mughal empire. Given Persia's very strong cultural influence in India and Central Asia OTL, it's hard to see it being much enhanced, even if a luckier Safavid empire conquers Central Asia and much of NW India [1]...of course, we might see a considerable extension of the region of Shi'a Islam in such a scenario.
Bruce
[1] These are, after all, pre-ethnic-nationalism states: the Persians aren't going to be following a deliberate policy of "Persianification" of the peoples they conquer.