Hi Garrett,
I remember we were talking about this by email years ago, when I was still a student -- and before you became kind of a web celibrity :-).
Concerning the topic of this thread here (to which I am arriving overly late, I know) allow me to say that I feel unsure about your proposed identification of physical fermions with BRST ghosts. To some extent the disagreement is just one of language, but that's not all.
I do agree that it is a good thing to ask: "What is a fermion, really?". Don't ever take any concept for granted.
And I do agree that the answer to "What is a fermion, really?" has to do with looking at graded structures.
But just as there are many groups out there but not every group one comes across is a gauge group, there are many graded structures out there and not every such is a BRST structure.
It should be clear that identifying BRST ghosts with physically observable particles is a contradiction in terms -- unless you actually only have some aspects of BRST formalism in mind but are secretly discarding others.
I think you are really essentially just looking at the graded algebra aspect of BRST. Which is good and fine. But shoudn't be addressed as "BRST".
I think there are two important sources of graded structures in physics: those coming from groupoidal structures and those coming from super-structures.
The BRST complex is, really, the (Chevalley-Eilenberg differential algebra of the) Lie algebroid version of what is called the "action groupoid" of the gauge group acting on the space of (on-shell) fields.
It is a fact deeply rooted in math -- essentially the Dold-Kan theorem -- that linearized (higher) categories correspond to graded complexes: the degree k of the complex knows about the tangent space to the space of k-morphisms of some n-category.
This is how N-gradings enter physics. And the BRST complex is the central example.
But all geometry that is out there also has a super-version. This introduces a Z_2-grading on top of everything else.
Now, it is a simple standard observation that a symplectic structure on an odd vector space is the same as a symmetric bilinear form. Hence Clifford algebra is precisely the Heisenberg algebra of an odd configuration space.
Just as L^2-spaces, the space of states of bosonic quantum theory, are the unqique irreps of the ordinary bosonic Heisenberg algebra, spinor reps are the reps of the odd-graded Heisenberg algebra.
That's what spinors really are: elements in an odd space of states. (Where "odd" means: graded by the nontrivial element in Z_2!) In the target space field theory context that you are looking at mostly, you see the "second quantized" version of spinors, where they no longer look like elements in a space of states, but as fields themselves. But that's just the magic of second quantization.
Now, the difference between Z_2 graded super structures and N-graded higher-order structures can at times be small, since lots of phenomena survive the passage through the homomorphism from N to Z_2.
This is the reason why spinorial phenomena can be seen also in BRST-like contexts. But that shouldn't make us go as far as saying that "physical fermions are ghosts". Because that's a contradiction in terms. It cannot possibly be true if both "physical fermions" and "ghosts" are used in the standatd sense.
Don't get me wrong. I think that your general approach to fermions (as far as I remember it) is all right. I just think that it is wrong to advertize it as being about BRST.
When you start thinking about quantizing your "exceptially theory of everything", or whatever gauge theory you have, you'll start wanting to use BRST-quantization of all the fields in your theory, including the fermions you have. They will have even (bosonic) ghosts attached to them.
