There's no standard and no way to say what is correct in linguistic theory. Linguists disagree about theory, and they always have. This talk about "standard theory" got started when Chomsky outlined some of his ideas and then said that henceforth he would refer to what he had described as the "Standard Theory". I have to think that he meant it as a sly joke. He proposes a name for his theory, for convenience of reference, as of course was his right, since it was his theory, but then, subsequently, anyone referring to this theory of his would have to call it "Standard", even if they just wanted to disagree with it. Get it? A pun on a proper noun. It's Standard (because that's its name), but that actually says nothing about whether it is standard.
No linguist was ever fooled by this cute little rhetorical trick, but it seems to have thrown a generation of linguistics students into deep confusion. No real linguist would ask the questions you've asked about what is "standard" and what is "correct".
Now, if you want to know whether what you've said about derivational stages in your example will make sense to phonologists, sure, it's perfectly clear. Appealing to intermediate stages of derivation was begun by Leonard Bloomfield, was controversial at the time (even for Bloomfield himself), became a routine part of Generative Phonology, then fell out of favor with some. But every phonologist knows how it works. That's not a problem. Do people agree with it? Some do, some don't, some don't care. Has it been designated as part of a Chomskian "Standard"? Who knows? Who cares? That's not a linguistic question.
As it happens, I don't personally believe in multiple steps of derivation, in either phonology or syntax. But I would never object to the sort of derivation you give in your example, because that sort of theoretical objection would presumably be beside the point of the analysis you're proposing. It would be irrelevant, and impolite.
If you're asking about style -- what is currently most fashionable among phonologists -- I don't know (or care).
I don't see anything wrong with your use of slashes and brackets. Generative phonologists routinely use slashes for underlying phonological forms and use brackets for phonetic transcriptions of any stage of a phonological derivation. What you have written seems quite clear.