For years, it's been obvious Iraq will split into three: Kurdistan, Shiastan, and a messy, Sunni-leaning middle. The policy should be to embrace and manage that.

1. Abandon the north to Turkish administration with UN observers. Yes, sucks for the Kurds, but Turkey is a NATO ally with a huge army, short supply lines, and a direct interest in stability there. This is an almost totally unused resource from the US perspective. Turkey still wants into the EU, a disincentive to anti-Kurd brutality.

2. Abandon the middle to Sunni control (as KFritz suggests), with sealed Syria/Iran borders.

3. Withdraw US forces to the south ("Shiastan").

This leaves all the oil under NATO control. It increases US force concentration by a factor of at least 5, simply by reducing the US-governed area. It leaves the US with a port city, minimizing the cost of supply and/or further withdrawal.

It ain't perfect, but this, folks, is a specific exit strategy.

The United States needs to mimic this strategy, at least in part. Our troops need to retreat to the perimeter of the country, seal the borders as best possible and watch the ensuing slaughter to determine which winning faction it ought to back as the new ruler of Iraq.
Special care needs to be directed to Iranian influence, and their proxy Syria. Oil production facilities of all types need to be protected as best possible.

If this sounds brutal, cynical, and Machiavellian, please formulate an alternative!