I saw this paper mentioned on Luke Ranieri's channel, "The Singing of Homer and the Modes of Early Greek Music," by M. L. West, and saw that he had notated a realization of what singing the Iliad might have sounded like. I made some audio for this if anyone is curious. I've attached a picture of the score that I made to generate the audio.

https://vocaroo.com/1oxfiyyCHX6z