I'm not sure St. John Chrysostom would have agreed that God's providence had much if anything to do with who won the hippodrome races in his day, though. But no man ever knows...
Arguably not, but he wasn't doing systematic theology as such, he was first and foremost a pastor in the truest sense taking up the call Christ gave Peter.
Your choice of Scripture doesn't suggest any are left to chance, although I would agree there does seem to be no clear and definitive statement from the Jewish Scripture exactly the degree of God's engagement in the world. I sorta have an understanding how practicing Jews today understand such engagement, but I lack your expertise and judgement about the matter in antiquity and would submit to whatever conclusion you have come to.
But if you look at the words of mine you quoted, we are in the world of the theological which has long run outside Scripture. If as a Christian you are willing to say God is not any one of the following: omnipotent, necessary, omniscient, necessary, benevolent, always active, then I guess you can get out of those difficult straits. (I think Scripturally you could argue some of the terms are not accurate, but given Christian tradition I would say you can't throw any out.)
Process theology is an answer.
This is one of the places (to take up a tangent that was going nowhere elsewhere) where I think Islam shows itself to be hardly more "simple" than Christian thought. I really wish someone could show me some decent overview of how Islam handles their extremely obvious and clear understanding that all comes from God and how they reconcile that agency within creation. As I have mentioned elsewhere, everything that I have read which takes this seriously ends up making as much sense as Leibniz's Monadology
, which while I admire, I have a hard time finding persuasive.
So if you have any suggestions about a great Islamic treatment of the matter I would love to know, as I think it could be somewhat insightful.