Puritan World Idea

After TL-191, Puritan World was my first alternate history, and one in which I immediately fell in love with. However, for those who know the time-line, the lack of liberal democracies and republics was a little depressing. So, I wonder if anyone had any ideas on how you could have a OTL America-like state in Puritan World, with a possible national independence date in the 18th or 19th century?

Theories I've thought about have been having England hold on to a colony or two, and another, more conventional American Revolution actually taking place, a Dutch Anglo-Boer state which declares independence, refugees moving to Australia, Latin American revolts, and even just adding islands. But, I'd like to hear if there are any other ideas.
 
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