AHC/WI: Adams wins the election of 1800

This is both a challenge and a what if. The challenge is to have a somewhat similar election to OTL (Adams and Feds vs Jefferson and Dem Reps) while having Adams win.

The what if is what if this happens? Is there any chance the Quasi War escalates into a full-scale War? Would the US buy Louisiana, win it in a war, or never expand past the Mississippi? Does this perhaps butterfly Hamilton dying away, and possibly pave the way for Hamilton to be elected in 1804? What are some other long term impacts of this?
 
Too help Alexander Hamilton’s presidency chances and to win 1800 for John Adams would be to have the pair united and working well together, rather than splitting the Federalist with the group of "High Federalists" aligned with AH.
 
Too help Alexander Hamilton’s presidency chances and to win 1800 for John Adams would be to have the pair united and working well together, rather than splitting the Federalist with the group of "High Federalists" aligned with AH.

What’s a possible POD for this?
 
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