Would it have led to questions? Surely not any more than the version they did use? On the face of it, "we lived together with dragons for a while until they betrayed us because they're evil" is not less plausible than "we travelled into this region and then dragons came out of nowhere and attacked us because they're evil". Both versions contain the possibility of a hidden act of provocation that contextualises draconic aggression as well. If you were going to concoct a false history to justify the war against the dragons, wouldn't you try to concoct a false history that is more convincing or more morally compelling than the truth?
Similarly for other issues. You mention extending the length of the ruse. If I wanted a ruse to last a long time, wouldn't I prefer a ruse that is as consistent as possible with visible evidence, and which requires me to convince the fewest number of people of new facts? If I want a long-standing ruse, a lie that explains the existence of ruins from a time of coexistence is, ceteris paribus, preferable to a lie that doesn't. If I'm going to try to undertake a mammoth task like convincing thousands upon thousands of people that they (or their parents or grandparents) didn't really live alongside dragons after all, I should at least have a pretty good reason for trying something so difficult and so implausible. Here, it seems like it only weakens the overall integrity of the lie by introducing new inconsistencies into it.
It's particularly baffling, to me, because characters in-game portray the issue rather bizarrely. Take Aymeric's confrontation with Thordan VII in 'The Sins of Antiquity'. Thordan says, "No reparations shall ever suffice. This fact alone should serve as ample justification for our actions, yet some refuse to see it as such. For men like you, who yearn to commit themselves to a nobler cause, a more compelling narrative is required."
The first half of that statement is, in itself, perfectly reasonable. Nidhogg cannot be negotiated with. No reparations are possible. The only viable course of action is to fight back. Lies about history are irrelevant when you're dealing with a berserk dragon driven by hate. The second half is very strange. They need a more compelling narrative in order to convince idealists to defend the people of Ishgard? Surely idealists are already committed to defending the many innocent people of the city-state? Thus when we got to patch 3.3 and the Final Steps of Faith, there was no issue whatsoever of people like Aymeric or Lucia laying down their arms, or fighting only halfheartedly. They believed Thordan I was a monster who provoked the war, but they still laid down their lives to defend the people. The lie has no utility.
Yet Aymeric's reply to Thordan VII is little better. "This is how you protect our people? You have given us a lost cause! A death sentence! With your compelling narrative, you but doom our countrymen to give their lives for a lie!"
Really? I thought they were giving their lives to defend their home and their people. I don't think I ever saw the Dragonsong War framed as a battle to defend the honour of the noble King Thordan. That always seemed secondary to the issue that Nidhogg wants to kill everyone. Thordan VII hasn't given anyone a doom that they didn't already face. There is nothing Thordan VII could have said or done to prevent Nidhogg continuing the war.
Which gets back to the wider issue, for me. So, if I take most of the game's description of history at face value... a group of people concocted an extremely implausible lie and somehow convinced thousands of people of it, they obtained absolutely no benefit from this lie, and then the lie isn't even a more compelling narrative than the truth! If you tell the truth with the sole modification of claiming that Ratatoskr struck first, or perhaps that Thordan I uncovered evidence of a pre-emptive dragon attack, or somesuch, you get a story that is just as good for everything you want the lie to achieve, and you don't need to convince everyone of an implausible false history. Why lie about centuries if you only need to lie about five minutes?
Well, I can try to think my way around parts of this.
Firstly, as I said, this makes more sense to me if dragon-human cooperation was not actually widespread, and that most of the population of ancient Ishgard had relatively little contact with dragons. Secondly, I think you have to reject the idea that all this lie was produced by a small band of conspirators at the founding of the high houses. If much of this narrative grew in small accretions over centuries, it seems more logical. (For example, why would the founders of the high houses lie in order to say that Thordan I brought his people to Coerthas after receiving a vision from the Fury? That story is irrelevant to anything they might want to say about dragons, and obviously false if told to contemporaries of Thordan I who have been living in Coerthas for generations.) Over a longer period of time, however, there's more room for legends to grow. Thirdly, well, I would just be deeply skeptical of anything anyone tells us about that time. I don't think I trust Hraesvelgr's or Nidhogg's accounts. Dragons are an oral culture, without writing (EE p. 269), both of them have strong emotional biases, and memories can be unreliable. So when I encounter something that doesn't seem to make sense, I try to be open to the idea that perhaps the story is inaccurate. The church version is distorted and self-serving, but the dragon versions may be too. Piecing together the truth is very difficult.
Well. Feel free to consider me mad, or simply obsessing over minor issues. I will do my best to reach the Scholasticate quests, though. I'm sure they have a lot of fascinating additional content about Ishgardian religion and history.