I would argue that the Federalists weren't so far off when they labeled the Republican Party "Democrats", and that's not just Hamiltonian newspaper saber-rattling there's Washington talking about how you can't make a republican out of a Democrat.
It isn't hard to see the parallel between Southern gentry that advocated what is in effect closer to democracy than republicanism (a loose confederation of states based appeals to the direct involvement of the citizenry rather than a quasi-monarchistic central government), and the parallel between the combination of this populist/democratic viewpoint, the agrarian radicalism of the early Democrats, combined with their planter aristocracy elitism as compared to the Greek propertied class who were the only ones with the franchise in the ancient city-states. This idea of "republic" as a democracy of the natural aristocracy, that Athenian democracy is great as long as you keep the leather working demagogues from gaining power.
Considering the parallels also with the Jacobins in France, how elitist factions that took power into themselves in the Directory were in some ways the establishment face of the Enrages and others in the mobs who wanted direct democracy, and with the Democratic-Republican societies; the first real political clubs; in the United States.
I'd say the Athenian American timeline would be one where the Democratic-Republican societies in the North during Washington's first term, before the two parties get going proper-like, last and flourish as much as the ones down south. Maybe even a presidency of Peter Muhlenberg of Pennsylvania. But primarily, maybe have Washington and his hate of parties keep his protege Hamilton from forming the Federalists, and the Democratic-Republicans are more aptly able to springboard the Democratic-Republican Societies in the North into having a strong presence nationwide, not just the South and New York. Plus participation in a war on Britain on behalf of the First French Republic could help radicalize the populace, as could Washington being president and getting us in the war on Britain's side.
Less intelligentsia-oriented, Shay's Rebellion or the Whiskey Rebellion could lead to more decentralization and directer democracy.
Basically, I think you need to link the existing tradition of the Democrats with the town-hall democracy types of New England, and I think the early Democratic-Republican Societies, which bridged the regions, are a good way to do it.
Also, I wouldn't downplay the influence Whig-era philosophers other than the proper and anti-democratic Whigs. There was a pretty populistic Presbyterian minister from Scotland from around Adam Smith's time who was an influence on some of the Founding Fathers in terms of his writings and political thought, I'm blanking on the name though. Early social gospel preachers could be a way to galvanize the direct democratic tradition of New England alongside the existing democratic ideology of the Democratic-Republican party and the Southern plantocracy.