Since it was an Ice Age, my guesses were the climates of "cold" "colder" "coldest with ice" and "coldest with dirt[no ice]" and "daaaannnngggg".
Further, it occurs to me that certain locations such as Miami and Palm Springs have not been sufficiently explored for evidence of early snowbird migrations, especially from the northeast. I could be convinced by a find of primitive golf carts.
All kidding aside, transitioning over 1000 years might not be that hard, given that the average age was 40yrs [or less!!]. Thats over 20 generations, or more if you accept a lesser average age.
These folks were nomadic....who knows if the herds they followed migrated hundreds of miles or not?
If a tribe was successful, it would have to split and those splinter groups would have to move a sufficient distance away so as not to impact the hunting of each.
So I think it COULD be possible.
But I am certainly no expert.
The life expectancy was probably more like 35 years, I would guess (and I really don't know), so that's even more generations.
Still, I don't buy a migration from proto-Alaska to proto-Patagonia, or even proto-Palm Beach, over a 1000-year period. Some of those bands which are nomadically wandering around are going to die-off, for instance. Others are going to find a comfortable valley and, not knowing that an even more comfortable valley is on the other side of that high ridge, will stay put. I'm not convinced that the population pressures are sufficiently high to prompt migration out of that comfortable valley.
I don't have a good hard argument yet. The Clovis hypothesis just never has smelled quite right.
Bye, Bye Beringia
(8,000 year old European Mummies in Florida)