Most such cultures wouldn't have survived 2250 years of technological progress, most of the languages that existed back then would have changed so as to be unrecognizable to most of the Indian tribes we know of today. Do you know of any culture or nation in Europe that survived 2250 of history? Are there any Romans, or Babylonians, or Egyptians? One might say the Greeks have survived, but they aren't the dominant culture in Europe, and the language the Greeks speak today is not the same language spoken by the Greeks during the Trojan War, I don't think Indians would be any different, so a lot of their new culture would be made up. These aren't the nature oriented savages that you are so familiar with. The Indians have learned new tactics in warfighting and have forgotten old ones.
Not sure where you are trying to take this. I was not disputing your premise. I was simply acceding to the point raised by others that this setting could be problematic if published.
Certainly, the cultures in North American would have continued to develop without Western European contact.
Of more interest to me would be what if the diseases that wiped out so many Native Americans, which made it far easier for Europeans to get a toehold in the Americas went the other way? What if the cultures of the Americas got access to horses, ships, guns, etc. but some disease that the peoples of the Americas were resistent to wiped out most of the European settlers and what if that disease was brought back to the Europe and wiped out a large percentage of the population of Europe and even, perhaps, parts of Asia?
The popular conception of North American First Nations cultures was created from the mid-1800s into the early 1900s. It is based on cultures that were already greatly transformed by the horse and by guns. Many of the settled peoples were already conquered, moved, and partially integrated. The camera had just started to be used widely and early photographers were travelling to the few remaining cultures that were still fighting for independence. These were were largely more nomadic peoples like the Souix and Apache and led to famous resistance leaders like Geronimo and Sitting Bull whose imagage were widely printed and took on celebrity status. But these cultures took such prominence and came to represent the "American Indian" in the European conciousness because the more settled communities had, for the most party, long been conquered and marginalized.
If you are looking to start with pre-contact peoples, it is more likely to be one of the larger, agrarian, settled peoples who had more complex governance models. Cultures who spread through conquest or through complex federated governance systems like the North Eastern tribles (the "Five Nations" a/k/a Iriquios league, later the Iriquois Confederacy). Personally, I'm more interested in the thought exercise of how these Longhouse cultures ( Mohawk, Onondaga, Oneida, Cayuga, and Seneca) would have developed if some time in the mid to late 1600s a plague were to kill off most of the Europeans. Given the Iriquois practice of taking in displaced peoples and their success in absorbing multiple groups under a federated system, perhaps the surviving French and British in the North East would have assimilated and that could help accelerate the transmission of technology related to guns, shipbuilding, etc. If plague was wreaking devestation in Europe, that could have given the Haudenosaunee ("People of the Longhouse") time to further consolidate power -- with an outside threat, there would be even more incentive for the tribes to come together in common defense and now that they had access to European weapons technology, perhaps they would not be able to repel the Europeans the next time. And instead of Colonization the relationship would be more about treaties and trade.
