Would explain sudden appearance across wide ranges.

http://www.ncdc.noaa.gov/cgi-bin/paleo/peltice.pl

This is a reconstruction of ice coverage for land. Over a short period of time (a few thousand years) after the last glacial maximum, the ice sheets shrank and sea levels rose dramatically.

So your "sudden appearance across wide ranges" correlates well with the existing population moving inland at that time.

The Barbados levels are probably the best index to use for what would have happened to any human populations in the Americas at that time. See page 4 of this article and look at the remarkable two-hump figure:
http://people.uncw.edu/grindlayn/GLY550/Fairbanks-Sealevel-1989.pdf
The thin double-humped line is the corrected time version. The sea was rising very rapidly at that time.

So your theory seems to match well with the geological evidence.

what they've found in North America. Tim Dillehay has one site in (I think) Argentina that is very old.
There is also the Meadowcroft site that is older than Clovis.

Monte Verde is an archaeological site in southern Chile, located in the northern Patagonia near Puerto Montt, Chile, which has been dated to 14,800 years BP. This dating adds to the evidence showing that settlement in the Americas pre-dates the Clovis culture by roughly 1000 years. This contradicts the previously accepted "Clovis first" model which holds that settlement of the Americas began after 13,500 BP.

There is plenty of evidence that Clovis wasn't first. They made such stringent requirements for proof of occupation (point lodged in animal ribs) that the proof just couldn't be met.
It's been some time since I read about the Chile site and I couldn't remember exactly where it was.

South Polar projection of the Earth. Kind of obvious when looked at it from that point of view. We're too fixated on our own hemisphere.

...it is way to late to account for the diversity of Amerindian language families. There had to be a whole bunch of migrations from Siberia and coastal northeast Asia for the last 20,000 years to account for it.

South/Central America? Ones they called the "Jaguar" people. Ignoring the fact that they looked like people who came from Africa.

if early Niger-Congo-speaking peoples had gotten to the New World we would know, since they were a very powerful, complex, and rapidly expanding culture with extremely high-quality iron-smelting techniques.

http://en.wikipedia.org/wiki/Nok_culture

there are other pieces of art in which the human figures look Japanese. I can post images if you want.
There's been no evidence that Africans came here and influenced the Olmecs. Some suggested that the bases of the pyramids at Giza are the same as those in Mexico. But many Mayan cities are built using astronomical measurements and the Golden Ratio (this is theorized).