Specifically ruled out in the OP.
Umm...
South Carolina's Nullification is allowed, letting States obey or not the Federal rules, leading to this situation after a couple of generations? This would, of course, require someone less ... resolute, shall we say, than Andrew Jackson to be President.
That could work, I suppose, especially if you got other states to sign their own Ordinances of Nullification.
I was going to say that all the Lord Proprietors could weather the Revolution and then split their possessions between numerous sons, like in Thuringia and Swabia, but that's too early. And too monarchical.
Maybe that time when the British burned the White House in the War of 1812 they could also burn/kill significant parts of the Federal Govt, meaning that states have to effectively self-govern for a few years, and by the time the war's over, they're very content with their new liberty and the new Congress etc. is as powerless as the Imperial Diet.
Also, maybe have the County as the base unit of governance rather than the State, so terms like "Massachusetts" and "Pennsylvania" are just geographical expressions, like the regions of Sweden.
Maybe if the Federal Government stays based in Washington as a sign of determination, but the British are able to capture the city anyway. With most of the central govt. prisoners of the enemy, the States would as you say have to effectively govern themselves for a while.
(Not sure how feasible it would be to have the Country as the main unit of government; given that the original thirteen States pre-existed the Union, I doubt they'd be willing to join it if it meant essentially voting themselves out of existence.)
Alternatively, maybe an even bloodier and messier Civil War could do it. Perhaps keep slavery in a few Northern States which then secede when the South does, or even engineer a three-way Civil War (by making New England secessionism an actual political force?), so that the conflict goes on for longer than IOTL and causes far more and more widespread damage to trade and infrastructure, large-scale refugee movements only adding to the disruption. Even though the Union is theoretically victorious and the rebel States are forced back into the Union, the country is left crippled by debt and the Federal Government lacks the will or resources to contemplate any meaningful military operations in the foreseeable future. Sensing this, the outlying areas increasingly start ignoring it and going their own way; and, when they are not stopped, the authority of Washington is eroded even further. Gradually Congress becomes a bit like the OTL UN or League of Nations, a talking shop with no real power to compel obedience to its decrees.
Any thoughts?