My continuance after the part you quoted disagrees with you, which I'll highly further as I'm replying to the other parts, but historically, yes, the characters appearing in the non-canon story modes would support your side of it, but SoulCalibur VI is a new paradigm where the story is concerned, I just don't know how you can't see that Libra of Soul is in tandem canon, but I'll do my best to expand upon the points I've made with what you've said back.
Except it is narratively related, which is why the unlocks for these stories are the way that they are. If they just unlocked naturally as the rest of the chapters in Soul Chronicle do, then they would have been spoilers for Libra of Soul. It was a deliberate decision to have them not do this until you have proper context by playing Libra of Soul, because it's all connected. If it wasn't, there'd be no reason for them to have arbitrarily locked only these two chapters.
The game argues with itself as to which mode you should play first, between Soul Chronicle and Libra of Soul, because Libra of Soul has the tutorials, so you'd think you'd start there, and you do also have to start there in order for your own personal rendition of The Conduit to appear in the main story Soul Chronicle (which might be why you may have missed that tidbit, if you play Soul Chronicle first, then Edge Master just brings out
a generic-looking dude in a brown hooded outfit instead of The Conduit, or, taken in a different way, this could be the "canon" version of The Conduit, though it is just a placeholder, from how I see it. But on the other hand, you have to finish the Soul Chronicle main story to unlock the substories for Grøh and Azwel, which definitely happens before Libra of Soul, so it's like, you have to start Libra of Soul, do the tutorials and make your character, get up to Edge Master's cave, then stop, go do Soul Chronicle so that you have the proper introduction to your character in the main story, then do Grøh and Azwel substories, then go back to Libra of Soul and finish it, then come back and finish Soul Chronicle, to be proper about it. It's a mess.
It's not directly stated in his Soul Chronicle, no, it would be an inference. But looking at the completed timeline, Zasalamel's self-monologues take place inbetween his interactions with The Conduit (again, see my screenshot from the last post), but Zasalamel admits to The Conduit in Libra of Soul after their last fight, where he realizes that The Conduit's power is not unlike Algol's, this:
"The Astral Chaos is a mire of confusion, an abyss both infinite and inescapable. It is power at its purest... and also the potential for change itself. Your power must have grown too strong, and your spirit resonated with and was subsumed by that of Algol. Another possibility exists, however... In my current life, I have examined closely the secrets locked inside my memory, and discovered a connection to fate, or "future memories" if you will,... As such, I am able to predict the destiny of people and the direction the world is heading. When I met you, however, I was at a loss. And so I entrusted you with the Libra of Soul... the spirit scales. Accordingly, the movements in the scales caused by your actions means there is now a discrepancy between my memory and the happenings of the world--as though an alternate version of history has been created. This truth has given me an invaluable clue, and helped me envision the next move in my plan. And if my conclusion is correct... things could get very interesting indeed."
Compare it to the lines from his Soul Chronicle:
"The cursed and spirit swords are together, and their power grows. Now is the perfect chance for those who seek power. It is time for me to take action. I once wished for death, but now I wish for something else. Now, I wish to cultivate the potential that people possess and lead them to a glorious new future. I seek not meaning or understanding in this. I am not even certain from which of my memories this thought sprang. I feel as if it has always been inside of me. Like a memory from a past life. I've thought of one other possibility. Perhaps this memory is from the future, sent back to me by my future self. ...Or maybe I simply have too active an imagination. Whatever the case, everything will begin once I obtain the power I need. The cursed sword and the spirit sword... I need them both to proceed with my plan. It has already been set into motion. The time has come. Now I shall harvest the fruit of my labors."
They are different, and yet the same. Zasalamel speaking to The Conduit is speaking in terms of the raw power that the Astral Chaos exudes, while Zasalamel in his study writing his books traces the power back to the swords themselves, but really, this is one in the same, as the Astral Chaos is where the swords draw their power, and the swords can be called forth from the Astral Chaos by those capable of manipulating its power (which is how it is that The Conduit is able to pull the swords to fight Azwel, and likely where Azwel got the idea himself to be able to pull forth Soul Edge for his new move from season two). Both speak of the future memories, the discontinuity between them and what has transpired, and both also refer to Zasalamel's future plans, so his interaction with The Conduit is what caused him to see the discrepancy with his memories, and changed his goals, is how I read it.
This is what happens when you go back to Soul Chronicle after you've played parts of or all of Libra of Soul. The key points of the story, where it relates to the various characters, those events get placed on the timeline, the same timeline that Soul Chronicle takes place in, a direct visual confirming the two timelines are one in the same. These are the "Hidden Records" from Museum, which also unlock as you are playing Libra of Soul. Basically, the story of The Conduit is contained by the Aval Organization, which is why the records are hidden, and why the world at large will not know of The Conduit and/or why The Conduit may not be referred to or return in the future, or, if they do, their story will continue to be held in secret, in all likelihood.
Again, you're relying on the way the previous games did things to prove your point, while my point is that they've made it very clear in SoulCalibur VI that they are taking the story far more seriously and actively not having these conflicts between different character stories. All of them work and flow together in one canon for Soul Chronicle, and Libra of Soul is also no exception to this rule.
I've already gone into Zasalamel, and I alluded to Raphael's last chapter being withheld due to spoilers for Libra of Soul, because Azwel is revealed to be alive and well. Azwel doesn't get defeated or "die" in his own Soul Chronicle, so there's no impetus for this unless Libra of Soul is canon and did happen, because The Conduit defeats Azwel, and he is presumed dead before the matter is settled with Grøh, to tie up all the loose ends. Both Grøh and Azwel have prologues in their Soul Chronicles, their actual story takes place in Libra of Soul, and then their epilogues are in Hilde's and Raphael's Soul Chronicles, respectively. The supporting evidence of Libra of Soul being the meat of the stories for Grøh and Azwel is in the Hidden Records being added, it's quite clear looking at their timelines what it represents.
Hilde's Soul Chronicle would confirm that the Grøh lives ending of Libra of Soul is canon, because otherwise he wouldn't be alive and sane to do what he did in her story. When you unlock and play Raphael's last chapter for the first time, it is shocking that Azwel makes an appearance, not just because it's he who is manipulating the scenes to come in SoulCalibur II and beyond with regards to Raphael's dark ambitions and Amy's turning into Viola, but that he's even alive to do any of that to begin with, because you played Libra of Soul, and he was presumed dead. It's a very logical flow.
I think we're safe from this, though, due to what I said above from Hilde's Soul Chronicle. I was just using this last bit to have some fun.
I've omitted this from the quotes, because I wanted to address it in its own right. You say begging the question, but all I've done is draw parallels between the modes and to me, it's quite clear and obvious that the two are in tandem with each other, by evidence of the game itself. If it was wild mass guessing without clear links between the two modes, I'd be inclined to agree, but it's been carefully constructed where it all flows together. The only way that they could have made it any more clear is if they also made Hidden Records for the side stories, for example showing the events with Plata and Talim's village on Talim's timeline, or if Amy was a character yet, she'd have her bits with Raphael on hers, or Raphael at least could have had those, because the Raphael and Zasalamel side quests are more important than the rest of the others, due to their literal linkage with the unlocking the final events to close the loop. Xianghua's parts are also weirdly missing, it feels like she should have had some entries like Kilik and Maxi, though Kilik should have had another one to bookend his, because he completes his training in his transformed state with The Conduit in his side story finale, it would've worked because the first book icon is the event from the main story represented in Libra of Soul. The list goes on.