So I just poked briefly through Wikipedia on the dates; your link suggests a time of ~200-300 BC for those writings, the Iliad ~760-710 BC. Given the slow rate of diffusion of ideas at the time, it strikes me as just as likely that even if this idea is true and the Iliad was written by humans with a profoundly different psychology than ours, it was some peculiarity of Greek culture rather than a universal human condition. The spread of consciousness at this time in history can hardly occurred that quickly.

(By no means am I claiming that these areas are entirely isolated from each other, but note the bandwidth of the cultural communication from the travel between them is so low that the net effect is that the various areas of the ancient world were basically unaware of each other. Even if some travelers occasionally made the hikes they didn't amount to much at the civilizational scale.)

And I find it far more parsimonious an explanation that this is just a crazy idea from a too-close reading of a work of literature that thematically chooses to be about "the gods" to imbue the work with mythic power, just the fact our culture has Star Trek does not mean that we have warp drive or that Gene Roddenberry's vision of happy coexistence has been realized. A fun idea, a great idea to build some sci-fi on, but not really a serious idea supported by the totality of the evidence we have from history, in which humans have been musing about the nature of consciousness for basically all of recorded history.