To answer your question, I'm no fan of Eric Shinseki, but I would have quadrupled the force immediately after the ground campaign had secured Baghdad. Historical precedence includes post war Germany and Japan. (Ever wonder why there was none of this nonsense in those two theatres?) I would then make sure that every swinging Tom, Dick and Harry engineer was drafted into the Army Corps of Engineers to fix the infrastructure (and for every engineer there should be five roughnecks/technician/electrician to do the heavy grunt work necessary). Finally, and I know I'll get pummeled for this (so be it, grrrr-woof) I would invite everyone to the party (that includes the French, Germans, Russians, Chinese and Japanese). The reason why we were able to rebuild Western Europe under the Marshall plan (unlike the slip-shod effort of the Warsaw Pact) is because we were able to marshal every resource needed to do so.
Which means you would have had a million US soldiers under arms in the Middle East. Where would you get them from?