A collection of opinions held with varying degrees of force and justification...
I am a Native American. I was born here. This is my home. My family has been here for centuries. Also, there isn't hardly a person in the South that doesn't have some Cree, Chippewa, Chicktaw, or Cherokee in him somewhere. Racism apparantly only goes so far, and it doesn't ever apparantly exlude the humanity of other humans enough to exclude sexual relations with them - sometimes even loving ones.
Well, the lack of a writing system in North America makes determining what real Native American culture like if anything even more daunting than finding out what real Celtic culture was really like. In both cases the problem is that all that is known is post-cultural assimilation, and in both cases most of what is 'known' turns out to have its source in material invented centuries after the culture vanished. And in both cases, this non-cultural material invented by the assimilating culture has been widely adopted as the cultural mythology of the people who are or who claim descent from the people in question. For instance, much of what is popularly held to be the meta-physical thought of the North American tribes was actually written or even forged by people of European descent in the 1960's and 1970's. (Very similarly, much of what is regarded as Celtic meta-physical thought was written or forged by non-Celtic peoples during the High Reinaisance - including everything we think we know about Druids, such as the Druidic mythology that inspires the D&D 'Druid'.) So, with that heritage in mind, I don't think you should be that worried about capturing the reality of North American pre-Columbus stone age culture.
I'm not going to bash North American culture here, but neither am I going to romanticize it. Alot of the most interesting things you can learn about the culture of North America comes from analyzing the oral language structure. For instance it is very interesting that not one tribe (that I am aware of) had a word for humanity collectively, and that each tribes word for person was also the name of the tribe specifically. But we won't go there.
The Pacific Northwest tribes are interesting and strike me as as different from the Eastern Forest tribes as the Eastern Forest tribes were from Europeans. Part of what makes them interesting is that thier assimilation occured late enough that people actually thought about recording it before it died.
I haven't a clue what was an accurate estimation of the death toll from Small Pox and Influenza. I'm not sure anyone does. No records were kept. All we can say is that it was a large number. Archealogical evidence is muddled because it is difficult to tell which civilizations collapsed for the normal reasons civilizations collapsed everywhere, and which where collapsing due to introduced disease. There is considerable evidence that some of the mound builder cultures were in decline pre-Columbus, but there is always disputes on dating. Probably North American poplulation had peaked a couple centuries before Columbus, but it is hard to be certain.
South America was less of a problem. They had writing. Of course, we can't read it necessarily - but they at least kept a record.
Tekumal was alienating because it was alien, not just because Central American culture is alien.