In my judgment, propositions are either true or false. Either this or that. I don't understand a proposition being neither true nor false. If a proposition can be neutral it seems to make no assertion or statement of fact. But this seems to be self-refuting in virtue that the proposition "all future contingent propositions are neutral" is not neutral.
I'm willing to make the model claim the law of contradiction obtains in all possible worlds; I guess that implies I shoulder the burden to prove the same for bivalence. Perhaps. But I too affirm God possesses non-propositional knowledge. I concur one can deny bivalence. I think open theists do this since they think it entails fatalism. I don't buy it. I think it's a logical leap.
The main contention with open theism is whether propositions of future contingents can be known. I see no reason to deny this. But what is the difference between a truth and a truth that is logically possible to know? The open theist is free to attempt to argue such truths are logically impossible to know. At best I think she can argue God does not know future contingent propositions but this is a far cry from the stronger claim it is logically impossible for Him to know them.
I do think the open theist conception of God is deficient. In open theism God is ignorant of many truths yet considered omniscient. Omniscience is taken as a model notion by the open theist when it is, in fact, a categorical notion. God doesn't merely have the 'ability' to know only and all possible truths; he knows only and all truths.