I tinkered with this a long time ago. My POD isn't necessarily very good, but it is to have one change to the original Articles: Only 10 states are needed to amend them (10 out of 13 or 3/4 later I assume).
This leads to a less drastic Constitutional Convention; the Articles are amended moderately and not scrapped. My suggestions were: President elected through exhaustive ballot by Congress for a 3-year term, possibly allowing two consecutive terms; increased power to create or expand executive departments;
Moderate Congressional power of taxation, domestic & foreign commerce; creation of a Supreme Court and federal court system; and maybe a few more. But not as extensive a list as the OTL Constitution. Meanwhile, every state gets one vote and the super-short Congressional terms may continue, as well as leaving up to the states most of the criteria for electing Congressmen.
Anyways, I postulate that a couple generations later there is a second Convention as the populous begins to demand better representation in the government. At this point you may get a federal structure fairly similar to ours, but with a congressionally-elected president and more deference given to the realities of political parties.
I am far from being an expert; I haven't read the actual Articles in years, so feel free to critique my take on things and use them as a springboard for any other thoughts
