Absolutely. I think this provides a decent summary: http://uregina.ca/~gingrich/n2f99.htm, though it is a bit heavy with reference to a certain practitioner of the "method", something I deliberately avoided. If you desire something more specific and in depth, I can send that info to you.
I don't have enough knowledge of the theory or the criticism to have any idea if your defense is appropriate to the attack. Looking at https://en.wikipedia.org/wiki/Structural_functionalism, I think my concerns about it would revolve around why "solidarity and stability" is used as the functional target, rather than something more fundamental like "individual competitive advantage". My worry would be that structural functionalism seeks explanations on the wrong level for the evidence it uses, much like "functional biology" could be led astray with evolutionary just-so stories.
As best as I can tell, you're trying to get at the coordination problem between theory and reality. That problem is usually phrased this way: how do formal terms and parameters in a scientific theory refer to features of reality? By themselves, the terms and parameters are just abstract structures with no empirical content. So, how are they given empirical content?
You kind of stumble through a bunch of semi-related topics, though. What have you been reading, if you don't mind me asking? Here's what I (Master's in HPS) would consider the most important works on the topic to read and digest:
There are lots of other relevant works besides these three, but they in particular are seminal and will point you to all the other stuff in their notes and bibliography anyway.
That said, I'll respond to a few of the specific points in what you wrote.
Formal theories seek to be redundant—they seek to be superfluous in so far as genuine redundancy can be achieved. Such a scheme would allow for one to superimpose their personal experience onto the logical structure of theory and yield an affirmative result (if the theory proves workable for that specific case).
Not all the terms of a theory will be directly connected to perception, even indirectly by measurement or by calculation from measurement. So whatever else it might mean to coordinate a theory with reality, it isn't some sort of one-to-one correspondence with observation. Even if it were, it's not clear what it means to "superimpose personal experience onto the logical structure." You also later refer to "concrete observable structures" being "isomorphic" to to "abstract theoretical structures." What are the actual operations involved in doing this?
This reciprocal correspondence between theory and measurement is really one between two higher level systems derived from, but not identical to, base reality. Both are subordinate to base reality. The empirical is not to be confused with the “real” as empirical data and its accompanying methodologies can be, and routinely are, faulty. Moreover, appearance is not to be confused with reality, nor are observations of those appearances.
You're sort of getting at something van Fraassen spends a lot of time on, namely that mathematical theories are usually tested by comparing them to data models, rather than reality "directly," and so there's a further question about how data models (which are also mathematical objects) are coordinated with reality. It's by investigating this question, which Reichenbach wasn't quite attuned to, that van Fraassen is able to pick apart and resolve issues in Reichenbach's proposed solution to the coordination problem.
More generally, the argument can be defined thusly: The description of all the statements which constitute a social systems theory as tautological is inevitable as they are all true in virtue of their form but not in virtue of fact. They need not bear any resemblance to the world, but only need satisfy the structure of the system and the logical minds who created it. The structure is coherent, but coherence doesn't necessarily imply a correspondence to reality, and hence the target of formalization. This can be called the general problem of formalization—as it applies to any science.
Last point I'll make is that I'm not sure where the argument you're criticising is coming from. Who says this? It seems like a weak version of something else, but I'm not sure what because the terms you're using to express it in this post are idiosyncratic.
The criticism is actually so loosely defined, and universally applied, that one of my express purposes in writing this was to articulate as best I could the criticism itself. And because of the universality of its application, it's brought up in most relevant literature as almost an obligation. Its lack of clear definition required my very own to be sort of "idiosyncratic". I think Formal Theory in Sociology: Opportunity or Pitfall? is one of the best introductions to the subject; and it happens to be what I was implicitly, at the back of my mind, referring to as I wrote this. (It's a fun read.)
Structural-Functionalism is usually criticized for being circular, in the following two ways:
1) The function of the whole follows from that of its parts, and the function of the parts follows from that of the whole.
2) Schematic representations of society are formulated on the basis of preexisting societal institutions which are, in turn, used to substantiate their existence.
The argument from tautological circularity suggests that this state of internal consistency prevents a formal theory from accurately explaining the actual structures and behaviors of the actual world; and that fitting the actual world into this scheme yields nothing but an artificial self-contained system divorced from all that it is attempting to describe and explain.
More generally, the argument can be defined thusly: The description of all the statements which constitute a social systems theory as tautological is inevitable as they are all true in virtue of their form but not in virtue of fact. They need not bear any resemblance to the world, but only need satisfy the structure of the system and the logical minds who created it. The structure is coherent, but coherence doesn't necessarily imply a correspondence to reality, and hence the target of formalization. This can be called the general problem of formalization—as it applies to any science.
The counterpoint to be made here is that the schematic representation is warranted precisely because it is based upon what substantiates its existence. Otherwise it wouldn't exist, and in its stead another possible version of it would exist. One which conforms to the actual structure of the actual world. Faulty premises derived from observations about preexisting institutions do lead to faulty formal theories and those that don't rely on faulty premises succeed in their intentions. What happens to be the case always remains, whether or not the theory succeeds in its intentions remains to be seen. The failure of a theory must be granted, but so to must the success of any given theory.
What qualifies as the criterion for success is where uncertainty arises. But this uncertainty need not be of consequence as the answer is simple: As long as a real world interaction, action, or organization satisfies the criteria for its counterpart in the formal theory and that formal counterpart implies the physical-social realization of it in the real world, then the overall structure of one matches the other. Just because the abstract seeks generality doesn't mean that particular instances of human experience and sociological phenomena don't fit into some general scheme. This scheme should mirror the particular, and the particular should mirror this scheme.
Formal theories seek a disquotational scheme in which reality, apart from its representation, can also fit. Otherwise no one-to-one correspondence between both theory and reality has been achieved. Formal theories seek to be redundant—they seek to be superfluous in so far as genuine redundancy can be achieved. Such a scheme would allow for one to superimpose their personal experience onto the logical structure of theory and yield an affirmative result (if the theory proves workable for that specific case). One can reflect their own experience onto the general structure of a scheme so as to see for themself how true to life a correspondence there is. The reader of these very words can themself act as an instantiation of a theoretical claim and so substantiate them. Only if this collection of instantiations is statistically significant enough will the claim made be substantiated. If not, the theory is a failure and the claims false. If it is the case then it is the case, if not then not.
The set of schemes should correspond to the set of real world particulars. I wouldn't say that the set of schemes constitutes the totality of a formal theory as that set accounts only for its structure and not its meta-theoretical parts—like why the theory is the way it is and how, which is to say the methodology of theory construction.
The criteria for success and failure that I’ve argued for thus far have been of whether instantiations of phenomena in and of themselves without their data representations are correspondent with their formal counterparts in some formal theory. The greatest consequence of a disquotational scheme, in which ‘X’ iff X, is that the object of study has been formalized into a sentential object—further divorcing it from the base reality of which it is intended to be a part. An alternative to my explicitly tautological approach would be to derive empirical evidence from observable real world events and functions, and consequently make structural claims about society based on the data collected; and view that as the only way in which to validate some theory.
What may be evident to some is the degree to which this resembles the problem of coordination in philosophy of science, which is concerned with how the empirical relates to the theoretical. “Correspondence” would be an appropriate addition to the vocabulary of coordination problems. This is especially so considering its present application to how theorizing relates to data. Coordination is comprised of both correspondence and validation. Validation for the theory that the measurement conforms to, and reciprocative validation for the measurement procedures that produced an outcome that the theory predicted. Because they correspond to each other, they validate each other. Coordination is reached if measurement M and theory T satisfy each other and it is not reached if they do not satisfy each other:
So coordination is a function of satisfaction as related to measurement and theory, and satisfaction is a relation between both measurement and theory. Success and failure are the two possible outcomes.
This reciprocal correspondence between theory and measurement is really one between two higher level systems derived from, but not identical to, base reality. Both are subordinate to base reality. The empirical is not to be confused with the “real” as empirical data and its accompanying methodologies can be, and routinely are, faulty. Moreover, appearance is not to be confused with reality, nor are observations of those appearances.
Satisfaction relies not upon the premise that concrete observable structures (the phenomena in and of themselves) can be isomorphic to abstract theoretical ones (substructures of models or parts of wholes); but upon the less committal and more plausible premise that data collected from instantiations of those phenomena can be isomorphic to formalizations of those phenomena. Whether correspondence between both the empirical and the theoretical does itself exist with the "real" is another question.
The argument from tautological circularity would also apply to conventional sociological analysis and any data driven discipline more generally. The data derived from empirical research is intended to correspond to what it is the representation of—just as a formal theory intends to do the same. This property of supposed circularity is not unique to formal theory.
Let me know if my criticism is as nonsensical as theirs.