I just finished Story of Your Life, and I disagree with your attempt to retcon it as a physically possible story; I think the evidence is clear that Chiang intended it to be understood the way that most people understand it, and that he in fact was misunderstanding* the interaction between the variational principle and causality.
[Spoilers ahead.]
Firstly, it is a really plausible misunderstanding. If you don't deeply grok how decoherence works, then the principle of least action can really seem like it requires information to behave in nonsequential ways. (But in fact the Schrodinger equation exhibits causality, and variational principles are just the result of amplitudes nearly cancelling out for all paths whose action is not a local extremum.) Chiang is a gifted amateur in physics, so this misconception is not that unlikely.
Secondly, if your interpretation were his intended one, he could have done any number of things to suggest it! Louise directly tells the reader that this story is being told from the night of her daughter's conception, and that she now sees both future and past but does not act to change it. This is shown in the story to be the point of Heptapod B, and Chiang works at length to try and justify how understanding this language lets one understand (but not alter) the future. There's nothing else in the story to hint that Louise is an unreliable narrator.
If your interpretation were Chiang's, he would have to be intentionally misdirecting the audience to a degree you only see from authors like Nabokov, and not leaving any clue except for flawed science, which is common enough for dramatic license in science fiction that it really can't count as a clue. I doubt Chiang is doing that.
And finally, the whole thematic import of the story is ruined by your interpretation; the poignance comes from Louise's existentialist fatalism, giving life to the lines of the tragic play she is cast in, which is only meaningful insofar as she's telling the truth about perceiving forwards and backwards. (It's a variant on the Trafalmadorians, though interestingly Chiang hadn't yet read Slaughterhouse Five when he wrote this.) It's just a more boring story the way you see it!
*Possibly intentionally misunderstanding; I can imagine a science fiction author pestering their physics friend with "I've got a great story idea using this concept", the friend saying "It doesn't work that way", and the author asking "But if I pretend it does work that way, exactly how much physics knowledge would it take someone to be annoyed by it?"
Secondly, if your interpretation were his intended one, he could have done any number of things to suggest it!
He did do any number of things to suggest it!
Nor do any of his out-of-universe quotes indicate he misunderstands. For example, just recently the topic of time travel came up on Hsu's podcast and Chiang says
...the first Terminator film does posit a fixed timeline. And you know, this is something I'm interested in, and yeah, there's a sense in which "What's Expected Of Us" falls into this category, also the story "The Merchant and the Alchemist's Gate" falls into this category, and there's even a sense in which for my first collection, "Story of Your Life", falls in this category.
Actually being able to see the future, in terms of information flowing backwards, in a self-consistent timeline is what is "What's Expected Of Us" considers; and "The Merchant and the Alchemist's Gate" uses physical movement backwards. What then, makes "Story of Your Life" not in the same category as either of those (especially the former) and in fact, doing something so different that it has to be qualified as the very vague 'even a sense in which'? (Because in "Story", the 'time travel' is pseudo time travel, involving neither information nor matter moving backwards in time, and is purely a psychological perspective.)
If your interpretation were Chiang's, he would have to be intentionally misdirecting the audience to a degree you only see from authors like Nabokov, and not leaving any clue except for flawed science, which is common enough for dramatic license in science fiction that it really can't count as a clue. I doubt Chiang is doing that.
I don't mind comparing Chiang with a writer like Nabokov. Nabokov is like Chiang in some ways - for example, they are both very interested in science (eg Nabokov's contributions to lepidopterology).
It's just a more boring story the way you see it!
I strongly disagree. Making Louise some sort of 'Cassandra' with handwavy woo quantum SF is thoroughly boring. The psychological version is much more interesting and far more worthy of 'speculative fiction' and Chiang's style of worldbuilding.
“Every season hath its pleasures; / Spring may boast her flowery prime, / Yet the vineyard’s ruby treasures / Brighten Autumn’s sob’rer time.”
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