(a) The definition I gave of a proposition is not too restrictive: it is the technical logical and philosophical definition. A proposition is a sentence that can be true or false.
In this case you will have to face the fact that you cannot decide if a sentence is a propostion or not. I cannot see how is this situation is better than to accept the fact that some propositions cannot be resolved. I am going to use the word “proposition” in this respect. A proposition is a sentence which “proposes” something, whether it can be decided or not.
(i) You argue that you are not claiming “The SM alone can determine the veracity of propositions” because it is self-refuting and besides you affirm that math propositions are clearly true and not scientific. This still leaves open the possibility that you maintain “Excluding math, the SM alone can determine the veracity of propositions about external reality.” Is that the case? You did say “The phrase ‘scientific method’ is just a misnomer. There is only one method.”
This is not what I am asserting either. The SM is the only method to arrive at objective true and false statements about the
external reality. In the deductive or axiomatic systems we can
prove if a propostion is true or false. In an inductive system we can “only”
substantiate a hypothesis. And to do that we need to either “verify” or “falsify” the result predicted by a hypothesis. Only predictions matter. You will always be asked to put your money where your mouth is.

When I say that the “S” is superfluous in the “SM”, I mean that if one makes an utterance (or prediction) and it cannot be decided, then it was an empty utterance, and as such it does not merit consideration. People make all sorts of predictions about God. For example I was told (far too many times): “Ask and you shall receive”. When I asked back: “when?”, the answer was “whenever God decides”. What kind of “prediction” is that? Empty, meaningless prediction. Don’t you agree?
My point has been one still has to justify extending the scope of the SM beyond its defined object to philosophical/metaphysical propositions about external reality. Additionally, if you are going to limit the scope of reality to physical reality you need to justify that.
I justify that by observing that the “non-physical reality” is merely a hypothesis. I am open to the suggestion that there is a “non-physical” reality “out there”, but I need the characteristics (attributes, properties, relationships, etc…) about this so-called reality. So far I only heard about this “non-physical reality”, but none of the details. True, you mentioned God, angels and souls, but merely mentioning them is not sufficient.
What is important for you to see is that to use an empirical method for investigating physical reality to check for what is by definition a nonphysical reality is a charade–it could not apprehend the thing even if it did exist.
No, you are mistaken here. It would be impossible, if that “non-physical reality” would
never interact with the physical reality. But the theist assertion is that there is an interaction. If there is an interaction, then there is an
interface. And one can “tap” into the interface - since it is at least
partially physical. Of course one could assert that the interface is pure, undetectable “magic”, but that kind of assertion will not be entertained. The conclusion is that as long as the non-physical reality
interacts with the physical one, it is subject to the observation, verification or falsification.
We already agree that, within the SM (including scientific projects and hypotheses) and computer engineering the immateriality of the mind [or existence of the soul] is not only an unnecessary assumption: more than that, it is non-existent, because the SM cannot pronounce upon it and did not evolve to investigate it.
I do not accept this on two grounds. One, you could justly point out that I claim “omniscience” (which I don’t have) and two, I do not wish to be accused of having a “closed” mind. For the time being, I treat the supposed “non-physical reality” exactly as I treat claim about the paranormal. I think that they are both bogus claims, but I stay open to the possibility that I am mistaken, and IF sufficient evidence would show that I am indeed mistaken, then I will happily “eat humble pie”. However, the burden of proof is strictly upon the proponents. I am under no obligation to refute or even answer some counter-claims. You are under obligation to substantiate them.
The philosophical assertion that the mind is immaterial is not a scientific hypothesis: it did not emerge that way in the history of philosophy and it is not maintained that way now.
And a successful instance of the Turing test will invalidate that assertion. If a philosophical claim is contradicted by a scientific claim, then philosophy
must yield. Also, if a philosophical claim says the same as a scientific claim, then what use is the philosophical claim? The only time a philosophical claim has a valid existence, if the question is open. And as soon the question is answered, the philosophical claim loses its relevance. And as long as the question is open, the philosophical claim is simply a hypothesis, which needs to be examined, just like any other hypothesis.
My gripe also is with asserting PA, a philosophical assertion beyond the methodological limits of science, without the requisite proof.
Since here we are outside the axiomatic systems, there can be no talk about “proof”. It is incorrect of you to ask for a “proof”. There can be talk about evidence, and the evidence is called the evidence of the pudding.