None of those were hunter-gatherer peoples at the time of European contact.
I didn't say anything about "... at the time of European contact." That's a part of your scenario.
Because it pretty much has to be. One of the greatest mistakes people make about indigenous cultures is assuming they were always exactly as they were at the time of contact, and that's nonsense. In reality, they're as dynamic and changeable as any culture. Perhaps more so in this case. These were mobile communities, interacting and trading extensively, with people moving from one community to another, communities going from more sedentary to more migratory lifestyle patterns as climate changed and rivers altered course, etc.
So if Spock was able to recognize the characteristics of specific communities, it stands to reason that those communities were taken from Earth around the time they were first documented by Europeans. Much earlier and they might've been too different to be identifiable -- particularly the Navajo, who were going through quite a lot of development and change during that period.
There's also the fact that, as I said, North America before European contact was a far more populous and developed continent than it was after European diseases devastated the population. So your premise that the Preservers would've sought a relatively isolated and "primitive" population would only even come close to reality after European settlement.
Besides, we know
what the Preservers' motives were from their own words. It wasn't just speculation that they were rescuing endangered populations -- Spock learned that by translating the text in their obelisk. As he stated it, "They passed through the galaxy rescuing primitive cultures which were in danger of extinction and seeding them, so to speak, where they could live and grow." And the only
time in known history when the Navajo, Delaware, and Mahican or Mohegan peoples would've all been in simultaneous danger of extinction was after European colonization. So the only possible time the Preservers could've taken those people from Earth was in the 17th or early 18th century.