@Arjen,
Chandler,
I agree with the ultimate grasp of your method and I think it is well founded. You move ahead, reasonably, to 1028a20. Also, Socrates is Socrates is definitely less questionable.
Putting your example up to Aristotle's framework, it makes sense to me (with the Socrates is Socrates substitution)
Socrates is Socrates
Socrates is mortal
That Socrates is Socrates in himself (Socrates qua Socrates) is right on. But I believe that to introduce "Socrates is mortal" is problematic because of the ontological nature of Zeta. We are looking for primary substance, and we both have the same idea, that there is something that is itself by itself. So when we see Socrates, we see Socrates as a whole, like we see apple, tree, or car. We know that car, tree, and Socrates have attributes (such as legs, arms, torso, head, blood, flesh, sinew, etc.) but we refer to Socrates as Socrates in himself (Socrates qua Socrates). So I agree with you totally on you interpretation this far.
That Socrates is mortal may be problematic, but definitely not wrong. That Socrates is mortal as an attribute of Socrates but not Socrates himself seems rational. Any attribute Socrates has, as we know it, has mortality? and will decay and die. But mortality is not a tangible attribute we can see on Socrates, it's an abstract concept that affects the attributes.
The first example is an example of a predicate and thing predicated of (substance). It's basically saying that we can perceive "a thing" and the "attributes" of that thing, and somehow, the two are separable. This is the first step Aristotle takes in revealing to us the nature of primary substance.