Evie
Pronounced like Eevee
The Iroquois fought both for and against the US in the War for Independence, ending a two-century-long policy of neutrality. It tore the Confederacy apart, from which they never recovered (a brief ascendancy of the Mohawk under Joseph Brant notwithstanding). To assert that Native-European relations were only destructive is reductive, but on the whole European Canadians, Americans, and Mexicans have been so destructive to Native cultures that to suggest that they are continuations of their indigenous cultures is patently offensive. They occupy the same geographical locations, but the population was replaced wholesale and left only small cultural influences on their conquerors. (To suggest Native Americans are disappearing is also patently wrong, but they are less than 1% of the population in the USA and for the most part live separately from the general population. Their cultural influence is negligible.)
I wouldn't lump Mexico with the Anglosphere Twins - Mexico's indigenous population numbers (without even touching the Mestizo and what indigenous ancestry they may or may not have) *dwarf* the other two, regardless of which way we look at it (I mean, there are nearly as many fluent Indigenous language speakers in Mexico as there are self-identifying Indigenous people in Canada or the US together, Mexican self-ID estimates range from twice to thrice the combined indigenous self-identifying population of Canada and the US). That doens't mean Mexico is good, just that it's a very different situation from the other two.
As for Canada and the Iroquois, likely no. Most scholars reject the thesis that any of the modern Iroquoian groups is directly descended from the Laurentian Iroquoians (which hasn't stopped both the Hurons and Mohawks from claiming it) - they seem to be associated with the Iroquoian settlements found further down along the Great Lakes. While Montreal was very likely part of Mohawk traditional territory for a great while, there's very little support to the claim that it's their place of origin or the core of their territory. Also, you know, proto-Canada (the French one) and the Iroquois spent a century at each other's throat, so not really the best mix. Besides which, if we want to represent the Colonial nations with Indigenous civilizations, the Cree have by very far the best claim to representing the region that would become Canada. And they're, you know, already in the game.
Back to the rest, I honestly think the Minas Geraes was an interesting choice and wouldn't mind keeping it, but if Brazil were to really get an alternate UU, then yes, the volunteers are the only good choice that's been proposed to date.