Sean, the OP shows that the reason Fr. Hewko wants the Holy Oil is for extreme unction: "Your Excellency, all I'm requesting are the basic tools for saving souls! Baptisms and Extreme Unctions cannot be given without Holy Oils (aside from emergency baptisms). Why would a differing opinion be an obstacle to receiving Holy Oils?"
When a soul is in their last agony, even a heretical, excommunicated apostate priest who hates and always slanders +Williamson can validly administer Extreme Unction. All I will say, and I hate to say it, is +Williamson will be in big trouble with Our Lord if it ends up that a soul in need of the sacrament does not receive it due to his decision.
As greatly as I respect +Williamson, he is gravely wrong here. He just is.
The ends don’t justify the means.
According to your rationale, every bishop is required to give oils to every priest who comes knocking, no matter what crazy and/or heretical positions he holds (eg., Pope Michael, or Palmar de Troya), simply because these renegades have duped some faithful.
But giving such renegades oils only enables their poisoned ministry, and THAT is what a bishop needs to worry about (particularly when Hewko’s dupes have many other priests from whom they can receive extreme unction, but choose not to). If they choose to exclude all those priests because of Hewko’s indoctrination, that’s on them, not Williamson.