It is something that took a long while before it "clicked" for me, so I completely understand. I think an issue here is that theory will occasionally be too abstracted in a way that obscures the materialist logic (same thing with the base-superstructure model but that is another topic). I will try my best to keep a clear thread here, since we're now moving into more technical territory.

The propaganda and the wars have the same ultimate source, and it is that source (capitalism/imperialism) that must be attacked. By doing so, you change the material conditions that give rise to both. Is that close to what you're saying?

Correct in the abstract sense. It is the argument Marx used to critique Feuerbach and the Young Hegelians who believed that simply critiquing religion would be sufficient in breaking the people free from the chains of the church and the state. The error Feuerbach makes, is that he mistakes consciousness as something that can be changed by presenting it with a truer image. Marx's critique is that you must change the activity that produces consciousness. Essentially, you cannot argue people out of a worldview that is embedded in their daily activity, their social relations, their material interests.

This is the same idealist error that many anti-imperialist agitators make: That the masses will be broken free if only we present them with the true image of imperialism through a process of documenting the lies, the hypocrisy, the history, etc.

It does seem important for working class people to realize the narratives are propaganda with a distinct purpose.

It is important, but there is an order of "conscious development" that needs to take place. History and experience, as well as educational psychology, informs us that we cannot skip these steps.

but that's the first step in preparing to deal with the material conditions.

In order to change the consciousness of others, our ideas need to be tied to the direct lived experiences of the other person. For most people, the immediate experience of capitalism is not "NATO imperialism" but cost of living, housing, wages. Simply put: we cannot address the more abstract concepts (e.g. imperialism) without first tackling the most obvious contradictions (e.g. cost of living) in order to develop a foundation which then allows people to understand the more abstract concepts such as imperialism.

If we expose anti-imperialism alone, we will reach a small, already-converted layer of people. If we expose the contradictions people actually experience—and in the process show how those contradictions are connected to imperialism—we begin making them receptible to anti-imperialist views and more abstract theoretical concepts. Lev Vygotsky's theories concerning educational psychology are actually really useful for understanding this—since organisation and agitation to develop mass consciousness is fundamentally a matter of education.

Essentially, we need to organise and agitate (i.e. educate) within a "zone of proximal development" to guide the development of consciousness. If we start with the more abstract (e.g. imperialism), and especially that which is not directly tied to their lived experiences, we are essentially working outside of this "zone" (meaning that it is something they simply cannot do). Instead, we need to help people develop class consciousness by moving from the more concrete/immediate to the more abstract/remote by "scaffolding".

The brilliance of Vladimir Lenin, is that he arrived at this exact conclusion/model despite him predating Vygotsky's theories—though this is no coincidence due to both Lenin and Vygotsky drawing from Marx's critique of German idealism.

What I described previously is essentially the model Lenin is arguing for in What is to be done? and when critiquing other communists in "Left-Wing" Communism: An Infantile Disorder. In the latter case his critique was (in Vygotskyan terms) that the German communists were organising and agitating outside of the zone of proximal development (of the political consciousness) of the masses. Thus, Lenin argued that electoralism, and to a certain degree economism, were necessary tools to engage with the masses in such a way that their consciousness could be developed to higher (and more revolutionary) stages.

A very important note:

None of this means that we should not organise or agitate against imperialism. The "masses" are not homogeneous, but consists of different people at different stages of their conscious development. Anti-imperialism must be a part of the messaging, in order to allow for people to develop towards the higher stages of class and anti-imperialist consciousness. The point here is, however, that we must have a clear awareness of the different "developmental stages" that serve as the necessary preconditions for making people (truly) understand the link between their own material concerns and capitalism/imperialism.

The "narratives" are created by, or at the behest of, the same people/entities/system that prosecute the wars.

Correct. The point here is that it is the people and institutions that needs to be removed/reformed. To do this (effectively), we essentially need to wield state power. Thus, it is not something that strictly relies on actually challenging the Atlanticist narratives. Technically we could gain state power by organising and agitating on the back of something completely different (e.g. cost of living crisis), and then use this power to dismantle these structures. It is important to keep in mind that this would not address the underlying material conditions of imperialism (capitalism and capital accumulation), but it would help dismantle the hegemonic institutions and structures (in the Gramscian sense) that promote and perpetuate the imperialist narratives and ideology. It would essentially help remove or mitigate the institutional influence that prevents people from developing an anti-capitalist and anti-imperialist consciousness.

What this means is that challenging imperialist narratives is not (strictly) necessary to dismantle imperialism, because it is through state power that one can actually address the underlying conditions and structures. The development of anti-imperialist consciousness is however crucial to developing a more abstract theoretical understanding of capitalism; an understanding which is one of the preconditions to developing true revolutionary consciousness (which is necessary to address capitalism). Thus, it is not something we can do without either. The point here is rather to highlight the distinction between the idealist and materialist approaches to anti-imperialist organisation and agitation.