I don't need to answer yours because the supposed "problem" doesn't exist. God isn't double minded, so when He says He desires all to come to knowledge of the truth, what more is needed?
—"What more is needed"? Context is needed. It is not talking about him desiring that absolutely all sapient sentients responsible to God be saved, nor even all humans.
—"What more is needed"? Reasoning use of language is needed. It is not double-minded for God to feel outrage at disbelief and to call it desire for the opposite (I say, supposing, for the sake of argument, that the verse was stand-alone, which it is not).
It means that whatever reasons a person claims to believe determinism are not actually related to their belief in determinism, should determinism be true.
Frankly I doubt very much that is what you mean by it, though what you do mean by it may be understood by you to be implicative of that conclusion. "Of their own accord" can mean something along the lines of independence from others of our kind, but it cannot be independent of God's causation.
I don't think you would say that your reasons not to believe in determinism are unrelated to your belief in free will.
You seem to misunderstand the argument, because it's not just that i affirm what I affirm, but that whether we affirm or deny free will we must do so on the basis of an act of free will. So in order to make an affirmation of determinism, the claimant must first demonstrate their affirmation to be false.
Confirmation bias. That we must (and do, constantly,) choose does not imply free will.