
This theory makes so much sense. It also makes you wonder if the 'song' the Wardens and Darkspawn hear is also somehow related to this. (if you subscribe to the Tainted Arlathan=Black City theory).
Everything sings, it's very eerie! I do think there's some relation there, especially if the origin of the Archdemons and Darkspawn is ancient elven, which seems very likely post-DAI. (I don't think the elves created the Blight, but I think they certainly weaponized it.) I don't really subscribe to Arlathan/Black City theory, but I have some thoughts on that below. 
It's definitely debateable. There are, I think, some dropped hints in DA:Asunder that something that had been buried beneath the earth escaped and created the Abyssal Chasm- something bigger and darker than the darkspawn that used it as a convenient path to the surface during the later blight. "...the chasm […] was a wound in the side of the world. Long ago, something had split the ground apart and let out something dark, something that lingered like the smoke after a fire.”
The description of the surrounding wastes is similarly leading: "It was a cold desert, mottled purple like an unhealed bruise. Rocky pillars jutted out of the sand like brittle, twisted bones; there was a sense that the howling winds had long covered everything else. Even so, it didn’t seem forbidding and horrible…. Just stark, and perhaps even a little sad. It was as if the world mourned a mortal injury inflicted long ago.”
Given what little we know of prehistory, I think it might be accurate to substitute the primordial entity "Earth" here for "the world". There's also the point that, given the relative apparent size and angle of impact the Tirashan crater suggests, the Pools could well be directly above where the Sun was theoretically imprisoned.
Add this to various theories about the Earth, the Stone, and the first Dark Ritual as well as Cole's cryptic allusions to The Prophecy II, and things start looking... kind of suspicious.
I could be wrong (I don't have the art book!) but I didn't think it directly states that the Tree of Peace was planted where Skyhold now stands, does it? Only that it was cut down to make the War Table before Skyhold's foundations were laid. There's actually a post about the Tree of Peace, the Avvar/Norse Yggdrasil, and the enormous cut elm in Frostback Basin over here that (to me!) makes a fairly convincing counter-argument.
I'd also be surprised if the Avvar had legends that touched on the Earth or the Sun, since I believe we're talking about primordial entities that even the Dalish can barely recall. In light of Andruil's ToM codex entry, I suspect the myth of Belanas relates to later Pantheon- specifically her red lyrium showdown here. From this perspective, the Lady of the Skies is more likely Ghilan'nain, mourning Andruil when she falls to dragon-form Mythal. (Which also fits a bit better with the Lady's direct connection to birds of the sky: in Dalish myth, those are the creations Ghilan'nain presents as a special gift to Andruil when she's elevated to Pantheon.)
Anyway, just some thoughts. Thank you again for the screenshot! The potential for a direct Sun connection seems much less likely with a title like "The Forgotten Ones", but the color of their vallaslin is still really interesting. Or worrying. 
The Pools of the Sun are over in Emprise du Lion, in the Frostbacks, they're hot springs. That's on the opposite side of Orlais from the Tirashan and the Nashin Marshes.
The description of the wastes in Asunder as unhealing is mostly referring to the lingering Blight, although as I said before, I suspect the rift in the landscape may have been the result of ancient elven warring. I'm still not convinced it's directly linked to the Sun battle though. Large scale warfare between the elves seems to have not been uncommon. I'm more suspicious of it being related to the Forgotten Ones, especially being out west, where we see more evidence of them (such as their worshippers in the Tirashan). The Forgotten Ones are also stated to dwell in the Void, which is equated to the abyss, which is typically used to describe the deep underground...which is also where the Darkspawn come from. There's also a particularly creepy place in Emprise that's hidden beneath Suledin Keep, which is ancient elven, like the coliseums nearby. The place down the hidden passage, a long stairwell that leads to a big black nothingness. Suledin Keep is also just across the way from the Pools of the Sun.
The part in the artbook about the Peace Tree:
Peace Tree and War Table
As a living tree, it was a symbol of peace between two forgotten factions. Before the first stones of Skyhold's foundations were laid, the tree was cut down, slabbed, and polished to serve as a massive war table.
It isn't explicit about the tree's location, but still seems implicit to me. There's also a picture of the tree before it was cut down, and it doesn't resemble the ultra huge trees in the Frostback Basin. Kinda looks like an oak.
I'll give you that Belenas probably isn't directly connected to the Sun business, though I still believe proximity to the Frostbacks and the former Peace Tree isn't an accident. The Pools of the Sun and the creepy abyss under the immediate area remains my prime suspect.
To ramble a bit about Belenas, as related to the previous post: Belenas, being Korth's old mountain, was according to the story in that codex, lifted into the skies, the Lady's realm. Yet in another older codex, there's also a story that it was destroyed, leaving only the crater that became Lake Calenhad. So which is it? Maybe both? To quote Cole about the rocks floating in the Fade, "they still remember when they were higher, before it woke up, and everything fell." What if Belenas was originally the mountain home to some elven god, and although it was physically destroyed, it still remains in the Fade, even if most of it is in pieces. Except for the city at the top, still floating up there...
This would have been well before Arlathan, since that fell long after the elven gods were locked away, presumably the Creators in the Eternal City (which may have gone boom), and the Forgotten Ones in the abyss (which may explain the sleeping Old God dragons deep underground).
(My other theory about the Black City is that it's actually deep in the planet, likely at the center by the means of the ancient elves' technology that allowed them to create pocket realms via eluvians. Because if the Fade reflects reality, if skewed, then something that could be seen from anywhere in the Fade would have to exist at some central point. Rocks in the sky might also suggest the Fade is presenting reality in an inverted fashion. The location would mean that it's impossible to reach in any conventional way aside from an eluvian that was specifically designed to access it (and if Masked Empire is any indication, would require a password), or directly hacking through the Fade, which was how the magisters did it, and Corypheus attempted to do again. In this theory, the Black City is actually the bastion of the Forgotten Ones, and considering that they dwelled in the Void with the Blight, and the Blight is what the magisters unleashed there, it adds up.)
When it comes to the Sun myth, the major question that muddles things is: Who and what exactly was the "Sun"? I'm doubtful it was literally the Sun, but I think something happened there. Whether it was simply an overthrowing of a power older than the elves (dragons? more elves?) or something more lost and obscure. If we really wanted to go out on a limb, maybe that was the Maker. Whatever he is. Back to the same question.
It feels good to ramble theories again.
The red vallaslin elves in the Tirashan are *very* interesting, since red is very *Blight* related now, and that just adds fuel to the fire that the Forgotten Ones were dabbling in the Blight to fuel their power...