I also have always found it improbable that a huge hunting group killed off the big animals. I say it was disease. These animals were isolated in the icy cold. Then it got warm and other animals from further south moved into previously glaciated North America bringing their diseases with them. Kind of like white man and measles.
My hypothesis on the extinction of the megafauna:
1. Clovis points are fluted. It can take several days to make a single spearpoint. Chipping out the concave channel takes a lot of time and effort, so there had to be a fairly good reason and big payoff for the effort. However, the flutes are perfect for adding poison to the spear point. Examples of readily available poisons are aconitine from monks hood flowers and nicotine from tobacco. For example, the Aleuts used aconitine to kill whales with harpoons launched from kayaks.
2. With an atlatl, a man can throw a dart about 100 yards, but not with the same accuracy as a bow launches an arrow. A single hunter could stalk and launch his poison-laden dart or a group could launch a volley. Killing a single mammoth or giant bison could provide food for a large group for days. The use of atlatls against herds of megafauna would provide a payoff that would justify the effort that goes into a Clovis point. Megafauna herds are easy to track. A hunting group could follow a herd until they had killed the last animal. Abundant food with few hunting fatalities would cause a human population explosion.
3. After the megafauna became extinct, the hunters had to learn new techniques to go after deer, elk, etc. Clovis points would not be worth the effort.
4. The transfer of this knowledge and hunting technique worldwide led to rapid extinction of megafauna over a period of a few thousand years.
Some problems with your ideas. Animals went extinct throughout the Americas, including almost all large mammals in South America, not just those who lived on the fringes of the glaciers.
Also these species had survived a number of previous ice age to interglacial movement over hundreds of thousands of years without going extinct.
Similar species in Eurasia did not go extinct when the interglacial hit.
There is no obvious answer to this, but I find it very intriguing.
In particular, there is some, though by no means conclusive, evidence that humans were present in the New World many thousands of years before this, as much as 10,000 years earlier or perhaps even more.