Is Buddhism A Philosophy Or A Religion? Imho, the source of the binary thinking is thought itself, how it operates.
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This is what Nagarjuna proves. The psycho-physical is a world-of-opposites for this reason ,since it is constructed by Mind. These are the categories of thought, and they would have to be transcended for Nagarjuna;s 'emptiness', the Unity spoken of in mysticism and the Christian doctrine of Divine Simplicity. If the source of binary thinking is thought itself (and not the binary world 'out there') then the source of the world 'out there' is thought. .
----"The evidence for this is that everything the mind touches gets chopped up in to opposing binary pieces".
Yes. It is not possible to think without using the categories of thought, which are binary. You're making many good Buddhist arguments; . .
For meditation it is not necessary to stop thinking. Rather, it is necessary not to follow ones thoughts. This is not an easy trick to learn.
--- "A possible problem with all of the above is that it's a temporary solution, not a permanent solution, much in the same way that eating lunch does not end hunger forever."
Yes. Hence Buddhism is rather more than just calming the mind.