I don't think that you are aware of anything not in the Neocon playbook.
The 2011 issue was about the status of forces agreement. The US has not had serious issues with those in the past. In that case, Obama told his negotiators to skip the negotiations. That is why there was no new SOFA and why US forces had to leave.
What I would have done in that particular point in time is not very relevant, considering that we would not have been in that position had we acted in a more rational way so far as foreign policy goes.
But if I had to be forced into that specific time and place, I would have negotiated a SOFA and I would have left US troops at 3 bases in Iraq. From those bases I would strike at terrorist targets at will. I would advice Iraq that our Jeffersonian Democracy fetish went away, and suggest they crack down on the population and control them.