To the OP: this basic theory has come up a handful of times over on the Lore boards, most obviously in the Dirthamen=Dumat dissection of the mosaic collections. The core conflict (and resulting identity crisis) runs deeper than that, though. If you examine religious beliefs found throughout Thedas, a persistent pattern emerges:
1) A new religion is established. Its earliest records suggest a distinctly humanistic bent with a focus on social harmony, free will, and balance.
2) As time passes, these beliefs seem to twist from the inside, the religion's tenets being used to slowly but ever more stridently exalt the rule of Order and its dominance over the individual.
This is true of what we know of ancient Elvhen practice, the Tevine worship of Old Gods, the Andrastean Chant, and the Qun. In the case of Tevinter and the Chant, the two we know best in game, both Dumat and the Maker seem to be the respective ropes in a tug-of-war between two oppositional philosophies.
In the case of Dumat, these sides are represented by Dirthamen-Falon'din and Elgar'nan. There's little doubt that when "Dumat" first came into contact with humanity the entity behind the mask was Dirthamen-Falon'din: his original, non-dragon form reflects Dirthamen's history, he came in dreams, he gifted humans with magic, he demanded no sacrifice or obeisance. That said, there's just as little doubt (in my mind, at least) that the "Dumat" worshipped at the height of the Tevinter Empire had been usurped entirely by Elgar'nan. His fingerprints mark every aspect of Dumat's worship: the focus on electricity, the twined double-dragon DNA motif, even the hexagonal beehive flooring and honeycomb-like furnishings in his temples.
I realize I probably need to write up a whole cosmogony walkthrough for anyone to take the above seriously, but the thought is kind of daunting. TwT It would be really, really long.
That aside, I would tweak your Tevine Gods <-> Elvish Pantheon association like so:
Dumat, the Dragon of Silence - Dirthamen
Agreed. While the "Dumat" that Tevinter worshipped at the time of his release was no longer Dirthamen, I believe Dirthamen's OGS was trapped inside the dragon they recognized as Dumat, and released when it was killed.
Zazikel, the Dragon of Chaos and Old God of freedom - Andruil
Andruil's personal history points to her existence as an agent of Chaos, a counterpoint to Elgar'nan's Order. This is also supported by Sera's perspective, if you adopt the popular theory that she's currently carrying Andruil's memory-wiped OGS. Stick it to the Big Hats, yeah?
Toth, the Dragon of Fire - Sylaise
This is probably accurate. Sylaise and her relationship to "fiery" Order is problematic, but the only alternative seems to be Toth as False-Sun-Elgar'nan, which gives him double duty in the Tevine pantheon. Not impossible, but much less likely.
Andoral, the Dragon of Slaves - June
Agreed. June's relationship to dwarves is particularly interesting here, since we have evidence that there was something distinctly disturbing about the dwarves' dealings with early Kirkwall and the massive underground prison in which we find Corypheus. It was clearly dwarven-built for another purpose long before the first Blight, abandoned, and then adopted by the Grey Wardens. One of the most telling points is in one of Corypheus' early lines to Hawke after he establishes they are human but not citizens of the Empire: he immediately assumes "slaves, then, to the Dwarves?" pointing to an age of human-dwarven relations seemingly forgotten in modern Thedas. Bonus crackpot theory: the local dwarven population unwittingly exposed themselves to red lyrium in their attempt to destroy Elgar'nan's focus (the red lyrium idol recovered from fleeing elvhen taking refuge in Cad'halash) and essentially became agents of his will. The timeline is wonky, but it's a compelling narrative and we have evidence at least some of the imprisoned were post-civil-war elvhen in the ancient murals found in a few of the cells.
Urthemiel, the Dragon of Beauty - Ghilan'nain
Ghil often gets shoehorned here simply because everything else seems like more of a mismatch, but ignoring her connection to beautiful, graceful halla, I think the case could be argued in terms of a different kind of elegance: her skillful mastery of genetics. The Chant revealed in WoT2 seems to hint that the promised "designs" may have been genetic in nature, further inferring that the Architect may be our most likely candidate for the Priest of Urthemiel.
Razikale, the Dragon of Mystery - Mythal
If there was ever any doubt, the JoH DLC has pretty much laid it to rest. Razikale's domain (and its point-by-point correlation with Mythal) is a theme that's hammered pretty hard.
Lusacan, the Dragon of Night - Falon'Din... or Elgar'nan.
Nailing down this association is rough. The primary problem with Falon'din's connection to owls, night, the moon, etc in Dalish myth is that it directly counters what I believe his source to have been. Dirthamen and Falon'din are two halves of a united whole: fragments of Order (Elgar'nan) and Chaos (the Sun) forced into the same body to create balance. From this perspective, FD is Chaos- he's the active, aggressive, impulsive counter to Dirthamen's contemplative, static status quo. Associating him with night, even assuming an inversion of his domain as part of his 'punishment', seems like a stretch.
That said, an association with Elgar'nan isn't impossible. His attempt to usurp the domain of the Sun, presenting himself as the False Sun, points to his true domain: darkness, night, void. Again, the fact that Dumat is already a convincing tug-of-war between Elgar'nan and Dirthamen-Falon'din leaves the door open for either to do double-duty in the Tevine pantheon.
To further complicate the issue, as always, each of these "gods" is simply a mask for a real entity: and one that doesn't necessarily map to the OGS-manned dragons we know as Archdemons. Since I think Falon'Din's powers are what make it possible for entities to be shuffled into and out of OGS vehicles via the fade, I'm not sure it's possible that he himself is inhabiting one in the physical world... meaning that between him and Mythal, we're either left with the one Archdemon we really, really don't want loose, or Elgar'nan never took dragon form and we may already be out of archdemons to distract the darkspawn with Blights.