I would say the Persian population and land is much larger than anything ever considered Greek, and they were throughly Islamcized. Have a quick Arab victory over Anatolia and that should do the trick. Using the Persian model, there were anti Islamic revolts for centuries after the conquest, independent Zoroastrian polities, and attempts to reclaim the Sassanid throne, but in the end, they became Muslim. The one thing that kept the Islamization going long after the Arabs left (they never really held direct control) was the non-Arab Muslim elite. By making Persian an accepted language of Islam, it helped to engrain Islam as part of the Persian identity.
The land areas is greater. The population . . . according to The New Penguin Atlas of Medieval History (this figure is from 737 AD for the record):
6 million in areas that can be considered Greek (possibly less depending on the size of the nonGreek Balkan population, but certainly at least five plus).
4 million in areas that can be considered Iranian (counting Azeribaijan). Five if Mesopotamia counts.
They really did hold direct control, or at least direct enough for the Persians to answer to the Caliphate until the mid-9th century (after that we see conflict).
And I think you're overestimating the interest of the Greek elite in converting. I'm not saying they would definitely not, but I think the history of conversion of Christians in areas ruled by Muslims OTL indicates that forcing conversion will not go over well, and merely "rule for centuries" isn't inevitably going to lead to Islamization taking over - even Egypt took quite a while for the Copt population to drop to minor.
As someone else posted, the areas of strong Zoroastrian resistance, Greater Khorasan and Taberstan, were rather far from Arabia and Damascus. Anatolia is much closer to Damascus than the Iranian plateau.
But its not so close that fighting rebellion is necessarily going to be easy or manageable.
Especially once you get past the frontier and towards the Marmara.