My thought would be to shut down one side at a time and keep it open for as long as possible.
By that, I mean keep the road open while rehabbing the bridges (perhaps shut down lanes on nights/weekends) and then shutdown as necessary to remove/replace bridges and then completely shutdown to replace the road. Then, tear out exit/entrance ramps in a sequence of first, third, fifth, etc. then second, fourth, sixth, etc. so you don't have to go to far if your exit is closed.