Trying for North America with no culturally American states. Point of departure is that the Vikings spread disease to the Americas, resulting in the great die-offs occurring in the 1000s and 1100s and the natives having regrouped, complete with some degree of resistance to European diseases, by 1492. This also means that some islands were totally uninhabited when Europeans arrived (Newfoundland and much of the New Hebrides died off completely, as did Vancouver Island) and some indigenous peoples wound up in weird places (the Nahuatl moved into Texas and Arizona).
The main feature of No America is that there are many small states, some ethnically homogeneous and others more diverse, that include both reformed indigenous nations as well as extensions and offshoots of European countries. The large indigenous population and their relative immunity to disease meant that there was no real room for pioneers, and therefore no real room for guns-and-agriculture pioneering. Instead, the European and later slave influx into No America was led largely by top-down settlement initiatives similar to those in Russia, Australia, and New Zealand, and No American polities of European and Russian origin are generally divided into dense urban settlements and tightly-organized farming areas surrounded by vast wildernesses, while a strong top-down urbanization campaign was an important part of the history of all the Plains and steppe polities. The color of the label indicates how strong indigenous influence is: the Union of Civilized Tribes, Nakota, Dakota, and Dineh are all self-governing nations that to some extent contract with Russia or Yurok for defense; Mishegon is an Amerindian-leaning multiethnic state similar to Bolivia, while Utah, Mexica, the Nuevas Filipinas, and Tahoma are all mestizo countries. On the other hand, New England is over 95% white Anglo, as Newfoundland and the surrounding isles were found utterly uninhabited; natives believed them to be cursed with plagues.
All of the key American stereotypes are averted:
-A large, space-filling power that is a major player in Afro-Eurasian geopolitics
None of these. They are all regional powers at best.
-A large federation that, while it might be ethnically diverse, generally shares a common tongue and flag
Only the UCT is a federation. The rest are all either unitary states or post-feudal entities, and five Indo-European languages are official in at least one state (English, French, Spanish, Russian, and Dutch). Instead of a Trail of Tears, many Amerindians were bribed to leave and have formed powerful Amerindian states such as Dineh, which is a mining state as rich as most of Europe.
-A major power that is markedly more capitalistic/consumerist/individualistic than most other countries at a comparable stage of development for much of its history (not necessarily more unequal, as at certain periods the capitalistic US was more egalitarian than the paternalistic countries of Europe)
Nope, nope, nope. The larger Amerindian population meant that state action was needed to acquire prime farmland on the continent and to formally acquire title, as well as to prevent skirmishes between the Amerindian and European peoples and to best utilize No America's rich farmland. Many of the Amerindian states also experienced top-down urbanization campaigns modeled after those in the 'Stans of Central Asia, and both European and Amerindian polities rely heavily on planned cities and planned infrastructure. Nakota and Dakota are essentially post-communist states.
-A widespread culture of self-defense/guns, agrarianism/suburbanization, and low-church religion
Nope again. The more urbane and centralized settlement of the No American states means that there are not the scattered populations that are associated with yeoman farmers and mass gun ownership. Instead, 90%+ of European-origin No Americans live in compact urban areas within 3-5 minutes of a police station, and the more concentrated (often ethnically stratified) location of farms in valleys or collectives means that farmland is too valuable to develop. Except for New England and Juniata, much prime farmland is still leased from Amerindian bands. And as for religion, there isn't really any room for Puritans and Pilgrims to settle aside from maybe the New Hebrides and the Aleutians. And the Aleutians are already occupied by extremely old-fashioned Russian Orthodox. Widespread gun ownership was cracked down on to assuage the fears of the Amerindian states that Europeans would lynch or shoot them, and because most people live in urban or compact suburban areas there isn't really the feeling that you need guns because the cops are too far.
-A cultural abhorrence of unelected nobility, royalty, regulation, or hierarchies not driven by ability or wealth
Ditto. There is a principality and an empire, and New England remains a commonwealth realm. Many of the chiefly families of the Amerindian tribes are effectively nobles. The population density and the historic need to balance European and Amerindian interests means that centralized government and regulation are very important.
-One of the world's dominant creative powers in technology, arts, literature, and film, with many if not most of the world's richest and most revered entertainers and innovators living there and a significant ceiling on one's success without doing business with that power
Nope. France and the UK are #1 and #2 on the Economist cultural power ranking, with Russia #3 and China #4 in cultural output. The most culturally influential No American state is Mexica, which is #11 worldwide, followed by Yurok at #15.