The individual colonies WANTED a weak central government. Getting them to agree to any such thing would be very, very difficult. IMO.
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OK, but this is a challenge. Hmmm....
How about George Washington dies early on, and someone like Benedict Arnold is the primary general.
Then, when the men are freezing and starving in winter encampments, with no response to stronger and stronger demands for supplies, the men start muttering about marching on Philadelphia and seizing what they need. Note that Washington had bad enough problems getting supplies, and Congress didn't fear HIM. The General in charge (Arnold, Lee, Gates, whomever) doesn't have the personal loyalties that Washington had, nor the sense of civic honor. So, firstly being unable to stop the men, and secondly not wanting to lose power, said general leads them in a march on Philly.
The Continental Army is in pretty bad shape, and loots 'requisitioning' supplies on its march. Some men drop out because they're too sick or weak, some because this is SO not what they signed up for, and some just flee as discipline breaks down - as it likely would in a mutinous army like this one.
Meanwhile, news of the oncoming horde strikes fear in the hearts of the Representatives, the citizens of Philadelphia, and most State governments. Philadelphia in particular, Pennsylvania in general and neighboring States raise and organize militias to meet the oncoming army.
In a close run battle, the State forces beat the diminished Continental Army. Most of the officers of the CA, and 'elected' leaders from the soldiery are hung
However. The primary reason for lack of supply was that Congress COULD NOT provide it. It didn't have the money or resources. This makes it obvious that a stronger central body (for at least war making) is necessary. Other reforms include constitutional limits on Standing Armies and an operational aversion to any single overall command. (Fearing a repeat.)
When the ARW is finally won (probably at least a year or two later than OTL), the US that results is a very different place. Much less hopeful and trusting. But the AoC is stronger.