I don't think such propositions have a single truth value: they are dialetheia, sentences that are both true and false.

As far as I know, they definitely could be dialethia, however I do think a when choosing between theories, I feel like posting dialethia probably should come with a greater theoretical cost then positing brute facts, but admittedly that's just an intuition.

Second (assuming you choose to assign only one truth value), there is no logical necessity to your choice.

I think I agree; what I suspect could be necessary is that the choice has to be made, but what the resulting choice actually will be I expect would indistinguishable from chance. Maybe, I'm misunderstanding something here.

On the other hand, I do think it is logically necessary that there is at least one brute fact* The PSR suggests there's a chain of explanations, but the chain must end somewhere - at an unexplained brute fact.

I might be talking past you, but I feel like I would more think of stuff like the PSR as concerning metaphysical possiblity rather then logical possiblity as I don't think there is anything inconsistent about denying or modifying the PSR. The hope with trying to secure brute facts within the realm of propositions and logic is that it might be a path towards really fleshing out resources that could be useful when wrestling with the problems found at the foundation of metaphysics.