I like one where Paine winds up as president. The war lasts four years longer and so many slaves flee to one side or the other that slavery just becomes impractical. No French revolution because we fight alone and the French government doesn't get overstretched. We get Canada except for Newfoundland, and of course, Florida was still British when we won independence in 1785.
Hamilton winds up with Treasury and tariffs are limited to ten percent, flat, on imports and exports. This pays for the army, the navy, and the university. We have a trimetallic currency. Most people do day to day business in copper, silver is mostly used by people in the merchant marine who have to deal with Moslem, Hindi, and Chinese trade, and gold is used for trade with Europeans.
I don't know who should control the navy. The navy is designed as a cruiser navy to destroy the trade of enemy countries, specifically England's. It is not designed to slug it out in line of battle in home waters. The large cruiser navy goes around the world exploring, mapping, pirate suppressing, etc. We have a huge merchant marine.
Jefferson runs the university in the national capital of Philadelphia and it gets ten percent of the federal budget, or one percent of imports and exports. The University is forbidden to teach theology or law, and explicitly directed to study agriculture, geology, manufactures, technology, etc. He also runs the national library and the patent office.
Greene gets the Army and winds up mostly doing Indian relations. We actually pay the Indians for their land instead of stealing it. Not likely, but I can dream. He controls the land expeditions we send to explore all of the continent. They also do the geological expeditions.
Adams runs the State Department. He spends all his time dealing in European affairs and making sure we stay out of them. He doesn't really do much with the rest of the world, because that's the navy's problem. He builds a world wide intelligence network and keeps us out of trouble.
New York is split between the Loyalist downstate and the Patriot upstate areas. All the interior drainage is dedicated to new states, including western New York and Pennsylvania.
Each state gets one senator, and there are nineteen states. Georgia, South Carolina, North Carolina, Virginia, Maryland, Delmarva, New Jersey, Pennsylvania, Long Island, Hudson, Connecticutt, Rhode Island (extending to what is now Maine), Massachusetts, New Hampshire, Vermont (with all of New York that drains north), Nova Scotia, New Brunswick, Quebec, and Ontario.
New states follow at a brisk pace, about one every five years. Florida, Kanawha, Erie, Cumberland, Ohio, Tennessee, Mobile, New Orleans, etc.
We buy Louisiana from Spain eventually. Then we buy California and the Colorado watershed. Then we buy Alaska. This happens about every twenty years.
Paine sets the two terms of five years tradition. After America has been set on the path it's easiest for Washington and Adams and Madison and the others to continue. There isn't as much infighting between Burr, Jefferson, and Hamilton because there isn't as much to fight about.
Paine appointed the Supreme Court to defend individual rights, and the consensus continues to go that way because universal voting means that the whole rich/poor infighting doesn't happen. Adam Smith's work is more widely read and understood, too, since there is four more years before the war ends for political climate to change.
Also, the longer war hurt the upper class more because they owned the properties that were more lootable by both sides. They also lost their slaves and indentured servants, and during the war they got their real estate confiscated by one side or the other, temporarily. What they got back wasn't in very good condition after the war.
Florida, Mobile, and New Orleans wind up as black majority states. Nobody cares. Eventually Texas and Colorado are also black majority. Again, nobody cares. It's too hot and malarial for settlement by white people without slaves to do the work.
Technological progress is far more rapid. This wasn't really planned. It just happened that as America grew, the navy and the university got more money every year. More money for the university attracts more students and professors. More money for the navy produces more agricultural and mineral specimens. Import substitution brings in lots of different types of craftsmen, and technology spreads and cross fertilises.
People like Winchester, Watt, and Faraday tend to migrate to America for the positions offered. This leads to America becoming the technological capital of the world as sort of a byproduct.
The coal mines of Pennsylvania cause steam railroads to be developed sort of as an accidental byproduct of horse drawn mining railroads. Philadelphia is rapidly connected to the Ohio river, and then the railroad goes north to lake Erie. After that it just spreads up and down the coast, and down the Ohio around the rapids. Steam boats take cargo to New Orleans.
Technological progress spreads in sort of quicktime, far ahead of population because the US trades around the world and new products are more profitable than old products with competition from old connections that the European countries built up over the last few hundred years. This also hurts Britain because they would have stayed at home as in OTL if not for the US sort of bribing them to immigrate with university positions.
The world trading empire that the US builds so quickly overwhelms and forecloses the kinds of empires that the Europeans built because the US is always there first. The navy doesn't stay here to defend the US because it is too far away to be invaded, let alone defeated, which is also why we have such a multiocean presence.
Without the Napoleonic wars to force consolidation, Europe stays in unconsolidated countries. Russia and France and Austria-Hungary and Spain and Britain and the Netherlands and the Ottoman Empire are the great powers in Europe, but plenty of little countries still exist.
Lots of little colonies are all over the world and still in the hands of the original owners, instead of Britain sort of scooping them up. Australia is pretty much the only colony as in OTL. The Americans got to New Zealand too quickly for the British to take over.