Hi, I wrote about your question in a different form - specifically Barnes' claim that Late Antique Romans considered Julius Caesar the first emperor - here. It may be of interest while waiting for someone to address your version of the question.

In short I think Barnes overstates the claim. I don't think the evidence he provides demonstrates that Late Antique Romans thought Julius Caesar was the first emperor.

One note about Julius Caesar and Augustus: they didn't have all the same powers. Notably Julius Caesar never held the tribunician power, no matter what wikipedia says.

EDIT: I've dug up a discussion between /u/xenophontheathenian and myself about the tribunician power issue.