Premise:
His Accidencty !,damaged goods but with a lot of popularity,sees reason agrees to run as VP to Winfield ScoTT in1852
The Whigs hang together
The FSA stays but can only be enforced by State
agreement in the North
Is civil war avoidable?
No, Fillmore in 1856 only won a single state, Maryland. No sitting President is willingly going to downgrade himself that way, and Fillmore offers nothing to the Scott ticket anyway, especially not regional balance as Scott has spent decades living in New Jersey and New York.
And your theoretical compromise just doesn't work, and would probably speed up the collapse of the Whigs.