Partition seems an easy answer until one considers the inconvenience of uneven oil distribution between the traditional Kurdish, Shia and Sunni areas. The Middle East has been a complex maze of competing ideologies and cultures for millennia. The advent of oil increased the difficulties of the region by orders of magnitude.
Daniel Yergin, in his book "The Prize" gives a fascinating history of oil and its ever increasing importance throughout the world from the end of the 1800's to present day. Well documented are the effects on foreign policy of decisions to change the British navy from coal fired to oil fired ships, coupled with an the increasing awareness of the value of air power and mechanized infantry. Britain had a secure source of coal in its lands. To change the fleet to oil that had to be sourced from other lands gained advantages in terms of speed and range of ships but came with costs of defending oil regions and the necessary shipping lanes to secure oil for the Admiralty and, accordingly, the resulting changes to foreign policy.
WWI proved the necessity of oil in the conduct of war to most heads of state and the procurement of which led to many post war decisions--not all of those well thought out. Three weeks after the conclusion of hostilities, French Premier Clemenceau and PM David Lloyd George met in London. France wanted oil--England wanted oil. So without consultation with either of their respective foreign ministers, George gave control of Syria to the French in return for the French giving up claims to Mosul. Clemenceau agreed provided the French received its fair share of oil production from Mosul. And so begins the competition for control of oil lands not only between corporations and other private business but now between nations as well.
So what to trade for a fair share of oil between the competing interests and ideologies of Sunni, Shia and Kurd. Areas with less oil will want what Clemenceau wanted--their share of oil in return for accepting traditional land with less oil.
I don't see a successful policy being forced on the people of Iraq. They are going to have to solve this themselves. And we will be living with the consequences for years to come... Sorry for the length but I thought some history might be of value when considering a solution. . .