Would you even need an organised, top-down attempt to change history? The story around heretics seems like it could arise quite naturally.
Suppose that a few generations into the war, some Ishgardians start agitating for peace, and want to negotiate with the dragons. On the face of it, this isn't actually a problem. Those negotiators will go off and either they will succeed (which is great; Ishgard doesn't have any reason to want to continue the war), or they will fail (in which case Ishgard has lost nothing). As it is, they will either encounter Hraesvelgr's brood, who will at best tell them to go away and at worst kill them, or Nidhogg's brood, who will kill them. A few naive kids lose their lives, and everyone gets a valuable lesson in the continued evil of dragons.
There's one problem. Nidhogg knows how to convert Ishgardian elezen into more dragons. Presumably this is where the idea of heretics comes from, right? Nidhogg's brood can reply to these idealists with, "Of course, let us tell you the truth, here, please receive our hospitality, drink this." Then they can start to produce aevises. Aevises are extremely valuable for Nidhogg: not only do they represent a reclamation of Ratatoskr's blood, they can provide intelligence on Ishgard, they provide more troops, and they provide an exit for any desperate elezen who may wish to surrender. After generations of brutal war, an elezen might despair and feel that the war is unwinnable. The promise that you can join the Dravanian Horde might be appealing, especially to any Ishgardians who might feel a desire for revenge against a nobility that is sometimes abusive or oppressive. You can even produce cults, so to speak: small groups of Ishgardians who collaborate with the Dravanians in the hope of one day being rewarded with ascension into dragonkin.
Once it becomes established that it is possible for people to cooperate with the Dravanian Horde, and indeed to become Dravanians, everyone else in Ishgard suddenly has a very good reason to try to teach everyone that cooperation is impossible. The person who wants to negotiate with the horde is no longer just an idiot throwing their life away, but a grave threat to Ishgard itself.
So of course Ishgardians will teach that it is always wrong to cooperate with a dragon. They tell stories about the depravity of heretics, and they will develop institutions (the Inquisition) whose job it is to prevent heretics. None of this actually has to be a deliberate lie. It's actually, well, true. For almost all of the Dragonsong War, there is no real hope of diplomacy, and the only attempts lead to betrayal, transformation, and slaughter. The best lies are built on truths, and so too here. In any case, once the concept of heretics is firmly part of Ishgardian culture, that will contextualise how you remember a figure like Shiva. If you are in a culture where you have extensive experience of people betraying their kin to join with dragons, and you are aware of ancient stories about the first elezen to join with a dragon, the connection is fairly logical.
Which then leads you to a pretty coherent view of Thordan's life, doesn't it? If dragons are all malicious, and they can recruit and transform people for their agenda, then pre-Thordan Ishgardian civilisation could easily fit into that pattern. A long time ago, there was an entire heretic civilisation. Then Thordan I destroys that civilisation and heroically separates out the races. Anyone who might object, whether dragon or human, by claiming that actually elezen and dragon once lived together as equals, can be seen as pushing a heretic agenda today. Heretics pose a real threat, so inquisitors will be rightly skeptical of anyone who preaches dragon-human cooperation.
This is a similar conclusion to yours, but it doesn't require any long-term project of deception from the top. I think I prefer a model where the view of history changes organically, from every part of society. The alternative feels too much like a conspiracy theory, to me. As I said, the best lies are based on truth, and I can well believe that the false history of Ishgard is actually 90% true.
As a side note, most of the above is about what I think of as 'Nidhoggian' heretics. Ysayle and her group are different. I might term them 'Hraesvelgrian' heretics. Nidhoggian heresy does involve transforming into aevises and is aimed at the victory of the Dravanian Horde and the destruction of Ishgard (e.g. the false Guillaime), while Hraesvelgrian heresy involves no transformations and is aimed at peace. It strikes me as possible that there have been many Hraesvelgrian heretic groups before Ysayle's, but they usually don't live for very long. Hraesvelgr's brood don't seem terribly determined to protect them, and Ishgardian persecution is relatively efficient. It is also worth remembering that, from the Ishgardian perspective, Hraesvelgrian heretics can be just as dangerous as the Nidhoggian kind. (Ysayle is responsible for attacks on large numbers of innocent non-combatants, after all.) I doubt anyone in Ishgard bothers to differentiate between types of heretics, but both types do present real threats to Ishgard.
On a side note, looking up aevises before, the EE notes (p. 288) that the word 'aevis' is from the Enchiridion, and seems to imply that the word was there before it was discovered that some elezen could be transformed into dragonkin. This doesn't seem to tell me anything about the composition of the Enchiridion - apparently it means 'devil who flies', and worshippers of Halone in the Fifth or Fourth Astral Eras had surely encountered flying voidset - but it is one more clue as to the contents of the text.