I think there'a a practical solution, There's only so many roads into Iraq from Iran. If I were a General, I'd take about 10,000 troops from stable areas in Iraq; reinforce those areas with more Iraqi units, then send the US trooops to patrol the borders, Syria too.
If you can find 10,000 troops that aren't needed to keep parts of Iraq stable, they will end up in the Sunni Triangle, where order is nonexistant.