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Aristotle's 'causes' as I previous listed are "final > efficient > material > formal"

You've got that bass-ackwards, LeGrande: Usually final cause is listed last, because it is the cause for which the others exist. As Aristotle explains (Metaphysics Book 2, Part 2):

"...the final cause is an end, and that sort of end which is not for the sake of something else, but for whose sake everything else is; so that if there is to be a last term of this sort, the process will not be infinite; but if there is no such term, there will be no final cause, but those who maintain the infinite series eliminate the Good without knowing it (yet no one would try to do anything if he were not going to come to a limit [peras]); nor would there be reason in the world; the reasonable man, at least, always acts for a purpose, and this is a limit; for the end is a limit.

The problem seems to be a confusion WRT the categorical distinction between a “final cause” in the cosmological sense, and a “final cause” in the phenomenal sense. In the former case, we have to speak of a telos — a cosmic, even divine, goal and/or purpose implicit in the primal form and subsequent evolution of the universe. Since this sort of thing can never come within the range of direct observation, it is not an object for science.

But “final cause” in the phenomenal sense does not invoke the idea of telos on cosmic scale, it invokes the idea of peras, "limit," the idea of finality of a process in nature. Such as a biological function.

As the mathematician Robert Rosen suggested, finality in this sense pertains to the necessary causal closure for efficient causation to depend solely on the resources of the “isolated” system in which it operates.

Rosen had a profound interest in biological questions, and in particular the ultimate biological question, What is Life? Rosen is coming at these questions from the “side” of mathematical modeling and complex systems theory. His approach culminates in a theory of “relational biology.” This theory presupposes that what is truly distinctive about biological organisms is not the “stuff” out of which they are made, but the way that “stuff” is organized: That is to say the Whole is never the simple summation of its parts.

Rosen maintained that any organizational system displays a pattern of causal entailment that can be mathematically modeled. And when we do model them, we find that simple, “mechanistic” systems in nature look very different from complex, “biological” ones. The network of causation tells the tale between inorganic (mechanical) and organic systems in nature.

Rosen describes causal networks in terms of all four Aristotelian causal categories — including final cause. In this, he knew he was breaking “the ‘Zero^th Commandment’ permeating all of theoretical science: ‘Thou shalt not allow the future to affect the present.’” He wrote,

…for centuries past, it has been part of the essential core of science itself that science and finality are incompatible…. [And yet] I am suggesting, on formal [mathematical] grounds, the possibility of separating finality from teleology, of retaining the former while, if we wish, discarding the latter.

In addition to getting the causal categories “backwards,” it appears that your use of the ">" sign indicates a temporal flow, or sequence. But Rosen noted that there is a “temporal anomaly…. Final cause cannot fit within the same temporal sequence in which the other causal categories harmoniously operate.”

As Rosen explained,

In completely formal terms, we may note that final causation appears anomalous, when compared with the other categories of causation. Formally, to say that something is a final cause of P is to require P itself to entail something; in every other case, to say that something is a cause of P means only that it entails P. Final cause thus requires something of its effect P; in all other cases, nothing is required of P beyond the passive fact of its entailment.

Moreoever, in addition to requiring its effect P to entail something, a final cause of P must entail the entailment of P itself. It is this peculiar reflexive character of final causation that is primarily responsible for its anomalous position….
In any formalism, there is a kind of natural flow from axioms to theorems, very much like the familiar unidirectional flow of time. Indeed, the formal analog of “time” is embodied in the idea of sequence, the order of application of production rules or inferential operations in proofs and algorithms. This flow of “formal time” is irreversible, just as real time is, and…for exactly the same reasons. In it, the axioms are always earlier than any of their consequents; a proposition P is later than another Q if it is implied by it, if there is a proof of P with Q as hypothesis.
The three “traditional” causes (formal, material, and efficient causation) always respect this flow of “formal time,” in the sense that “cause” Q always precedes effect P. Final causation gives the appearance, at any rate, of violating this flow, in the sense that the effect of P seems to be acting back on the causal process that is generating it; it appears that the “future” is actively affecting the “past.” I say “appears” because this (traditional) interpretation of finality confuses P with its final cause; it is not the effect P, but the final cause of P, that must operate on the process by which P is generated.

And thus the temporal anomaly remains.

First cause (a/k/a "uncaused cause") refers to cosmological concerns with origins. It is “needed” to obviate the problem of infinite regression — just as the cosmological variant of final cause (telos) is concerned with obviating the problem of “future” infinity (if I might put it that way). “Infinity” is an extraordinarily valuable concept in mathematics — and yet it has been found to be “unconstructible” in the physical sciences. And thus “first cause” is not a problem for science.

Well, for whatever the above is worth to you, dear LeGrande. Methinks there’s more to “final cause” than has been “dreamt of in your philosophy.”

Unless you're actually right about knowing more than Aristotle and Newton.... If so, you have yet to make your theory intelligible to me.

Thank you so much for writing!