Composition Of Iraq Challenge 2.0

I earlier posed the challenge of producing a source for Juan Cole's claim: "Sunni Arabs .. in Iraq .. are 20% at most". The unstated reason I had strong suspicions Mr. Cole is talking hot air this time was: I knew Censuses in Iraq were conducted without a question on religion (nor was a normal sociological sampling possible during Saddam or the Occupation).

In the Comments, EuroGaullist confirmed this by digging up the story of, and data from, the latest Iraqi census: the one of 1997, kept under wraps by Saddam, but parts not looted or burnt handed over to the UN on 8 August 2003 by the American government. After a little digging around, I found regional maps based on this census - which allow me a very rough guess, based on the generally reported regional distribution. With the approximations that

1. the Sunni Arabs South of Baghdad and along the Saudi border can be matched up with Shi'a Arabs to the North;
2. the Sunni (and Shi'a) Arabs in Kirkuk can be matched up with Kurds to the South;
3. Niniveh province (included Mossul) is at least 20% Sunni Arab and 30% Kurd;
4. Baghdad is half Shi'a Arab;

I get: out of then 22.1 million, 48% is Shi'a Arab, 28% is Sunni Arab, 19% is Kurd, 5% rest. (Note: data is missing in two 100% Kurdish and one 100% Sunni districts.)

So, again: I dare you to find a source implying numbers anything like Juan Cole claims!