Hardware is just software on a higher plane of existence
The main difference seems to be that we think of physics as having a fundamental level at which it has total causal closure, whereas software is conditional on mutable properties of the substrate.
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Yes, that is exactly correct. Assuming the thesis of causal closure is true, it follows necessarily that hardware and software are decidedly different, thereby invalidating any attempt at reconciliation. But that is also kind of a loose assumption...
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It is just an statement about write access. If you live in a software that does not offer access to the underlying hardware, that software is causally closed as well.
End of conversation
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