So one of the issues in terms of why you aren't finding anything is that the events you are interested in are pre-historical--that is, they pre-date any sort of historical records, at least in that area of the world. You will have to rely, then, not on written histories, but instead the historical sciences; specifically, historical linguistics, archaeology, and genetics.

Another issue might be terminology. You seem to be approaching it looking for “Zarathustra’s people” or the Avestans. While they were important, there are certainly other Iranian peoples. The Scythians, for instance, were attested in ancient Greek sources as far back as the 8th century BCE, and though the evidence is limited, we can be fairly certain that they spoke an Iranian language. And in any case, these attested cultures are much later in time than when we think there was a unitary Indo-Iranian people. This would have been somewhere around the 3rd millenium BCE.

And to comment on the linguistics portion, historical linguistics is a historical science. We don't just "speculate" or guess about stuff, we have rigorous methods which can tell us quite a bit about the past of different languages and the people that spoke them. We need these rigorous methods as there are several reasons why languages can have common traits.

One is that elements of languages can just look similar by chance. For instance, many of the world's languages have a word order of Subject-Verb-Object in simple sentences. Swahili and American Sign Language, for instance, both share this word order but are not otherwise related. Similarly, English has the word mess, and Kaqchikel has the word mes, both pronounced more or less the same, and both meaning the same thing. But English is not related to Kaqchikel.

Another is that languages can borrow from one another. This can tell us about what groups were in contact and when. For instance, if we didn't have any other knowledge of Japanese and English, we could tell that they were in contact because there is borrowing both from Japanese into English (for instance, Eng. sushi from Jpn. sushi), as well as from English into Japanese (for instance, Jpn. mai-kā 'one's own car' from English my car).

Finally, we have what linguists call a genetic relationship. That means we've ruled out every other possibility for similarity, and we are left with similarities that can only be explained by a shared history. For Indo-European languages, work has been done, ostensibly, since the 1700s. We know that the Indo-Iranian languages, the group you are interested in, do form a valid group. We know this because they share some traits that no other Indo-European languages share. For instance, Proto-Indo-European, the common ancestor of all Indo-European languages—including Indo-Iranian languages—had the vowels *e, *o, and *a (the asterisk here means that a form is reconstructed, rather than directly attested). In Proto-Indo-Iranian, the common ancestor of all Indo-Iranian languages, these all merged into *a. So, for instance, Proto-Indo-European *k^(w)e ‘and’ would become Proto-Indo-Iranian *ča. And we find this directly attested in Sansrkit as ca, and in Avestan as ča. We only find the merger of *e to *a, for instance, in the Indo-Iranian languages, so we have good evidence then that they must form a coherent group.

And as Indo-European is probably the most studied and longest studied language family, I think that many of the conclusions historical linguists have reached about it are fairly safe.

It's not exactly that PIE can't tell us about migrations, it's just that in the 21st century people are more sensible about tying proposed linguistic groups to archaeological evidence without some firmer form of corroboration. We're...weary. Whenever anybody speaks of such things in terms of certitude (as a lot of pop books tend to) you know you're dealing with an idiot/madman/someone deliberately disingenuous.

Ok imagine a schema like this. We know these languages (early Indic and Iranian) are a) derived from an older language and b) share an especial affinity with one another. At one point there must have been a higher order grouping, Indo-Iranian, which split up into Indo-Aryan and Iranian. This much is clear.

Now what does that tell us about religious attitudes/civilisation? Nothing really. We can't infer back what attitudes they had, we can't even assume uniformity across either group of people.

Earlier scholars were caught by an interesting apposition between Vedic and Avestan deities where each group posited a distinction between Devas and Asuras. For the Indians the Devas were gods, the Asuras demons. For the Avestans Devas were demons aligned against the god Ahura Mazda. So some tried to explain the split thus.

Highly problematic! The Asuras are hardly "demons" in early Indic thought. Moreover the split assumes then that all Iranians = Avestan, which certainly isn't the case. In other words Zoroastrianism was a later development, post split, the split wasn't a major event but a series of divergences and convergences amongst nascent dialect groups tbh.