You don’t need to keep bringing up the Overkill Hypothesis. It’s a forty-year-old idea that has been out of date for the past 20 years.
I think then that the issue is just confusing “overkill” with what the Australian researchers and others are talking about nowadays, that man committed a coup de grace in the past was not overkill, but it left many species dead regardless.
The problem is that “overkill” is sometimes used as a synonym for “unsustainable hunting” as in the article you linked to. It really just refers to Martin’s “blitzkrieg” idea of a wave of intensive hunting wiping out the megafauna in a single area in a generation. Long-term lower level hunting, or what was sometimes referred to as “sitzkrieg”, is more likely to have played a role in megafaunal extinctions.
By the way, I heard Martin introduce his ideas in a lecture he gave at the University of Colorado in the late 1970s, I think before he published them. I thought it was a cool idea at the time.