One stand-out issue with the premise of "populations have to migrate, but then agriculture comes back elsewhere" is that our currunt interglacial has a high degree of long-term climate stability. There is a lot of evidence that during the glacial period, the entire planets saw a mucht higher frequency of climate shifts.
Meaning within time-frames of mere centuries.
The current theory is that this is one reason why agriculture kicked off about as soon as we entered the interglacial. The opportunity was there. Finally, the climate was stable, which meant a society could settle in one place where the living was good... and it
stayed good. So they didn't have to up and get going a few hundred years later. This gave them the prerequisite time to develop a more sedentary modus vivendi.
There is good reason to believe that this is a pretty fundamental pattern, which means that a new ice age will cause renewed climate instability, which means -- well, that humanity goes back to the hunter-gatherer stand-by. Because under such conditions, that's the only sensible and viable way to exist.
If the new interglacial starts in 1980, then the next centuries will see small bands of humans settle down in favourable locations, and invent agriculture.
In other words: the period 1000 BC - AD 1980 is a second
Younger Dryas.