Not quite. In some games he is represented differently. In FFXII, for example, he is not a demon, but an Esper that was created by the gods. He is called the "walker of the wheel," which was a reference to the cycle of life. He was born into the chaos of creation, and was killed and reborn several times until he was able to meditate on the cycle, reducing the anarchy to nothingness (its no wonder he was pissed at his creators).
This is actually not as sketchy as you might think. The series writer Kazushige Nojima reportedly confirmed in a guide book that the two games are, in fact, related to one another. He elaborates further to say that Shinra (FFX-2) never gets his experiments to work on Spira, but his great descendants finish the job on Gaia (yes, after traversing through space to get there) 1000 years later. This was taken straight from one of the writers, so unless someone made a MAJOR mistake translating that article, it's a fact.
I suppose that's a fair point... but I really don't see why anyone should leave Tactics out of any lore discussions. Regardless of how loved or hated that game is, and regardless of it being a "side-game," it's still a Final Fantasy title, and the lore of the FF Tactics game was used as the ground basis for FF XII (a "Main Series Title") as well as numerous other games in the series. Considering that there are things that are either literally copy and pasted straight out of that game, or heavily influenced by the events and lore of that game, there's no reason to leave FF Tactics out. I'd actually say that ignoring Tactics lore makes any lore discussions far less credible, because SE has been blatantly taking influences straight out of that game, especially for FFXII and FFXIV.
That's my mistake. I wasn't clear in my typing. The Crystal Tower falling from the moon is part of the fan theory. The idea was that the first Lunar Cry mentioned in FFVIII would serve as the event, and it's backed up by comparing the geographical information between both world maps. The Fan Theory highlighted the places on the map in which the Crystal Tower was, and the craters where Lunar Cries supposedly happened, and one of them lines up in some way (where Adel tested it in Tribia). The more convincing part for me was the fact that the crystal tower was within Lunatic Pandora in the first place. That seems to imply a link, especially given that the tower serves as the basis for a gateway. The Lunar Cry could only occur when the it was in alignment with the moon. Like I said, it is a bit of a stretch, but it's interesting that there are such coincidences that line up so nicely.
Another interesting point is that in different versions of the game, "Hein" was actually corrected to "Hyne." It may be semantics, but the two names are often switched with one another.
More important is the similarities in the lore between the two. Hein (FFIII) and Hyne (VIII) were both known to be the origin of the sorceresses. Further, when Hyne splits his body in FFVIII, he is said to have merely given humans his skin which would make him skeleton identical in description to FFIII and XIV.
Hein's minor role in III isn't really a breaking point of the theory either. Given the stories are unrelated, Hein does not require a big role to have larger lore implications in VIII. In fact, the lore of FFVIII has bigger Hyne implications for III than it does for it's own game, because it implies that they Hein you fight in III is not actually the real Hein. It's only a piece of him which he cast off back when humans first rebelled against him, which is why his head goes missing at the end of the fight. Even if the W'soL managed to kill Hein in III, it wouldn't matter, because there are still pieces of him out there living in the bodies of young women.
What you said of SeeD is true, but that doesn't change the thematic similarity. The point is not who created SeeD and why. the point is that children are fighting wars against magical beings. The Warriors of Light go by a different name from the SeeD's, but they were still children. Hyne is the origin of the Sorceresses in this conflict, and Squall is the origin of the SeeD, as an organization. That does not mean that people (children or otherwise) were not fighting against sorceresses since long before the SeeD were established. Laguna, for example, fought against Adel and wasnot SeeD.
Again, it's not rock solid, and I'd have to play III again to pick out whether or not I agree with it, but there is quite a bit of evidence to support it. In the end though, like you said, it's just one of many possibilities.