Why not just have major contractors required to post a bond when they place a bid, and if they have cost overruns they pull those from the bond (ie, their own money)?
Case in point: SpaceX challenging the launch industry's cost-plus culture with publicly-posted fixed prices [1].
Case in point #0: the Space Shuttle (STS).
[1] https://www.nasa.gov/pdf/382045main_19%20-%2020090730.11.STS...
Cost plus percentage gives a very clear incentive to raise costs
And had the competing team won, the Challenger disaster never would have happened, because the solid-rocket boosters would have been manufactured as units and transported to the Cape by barge rather than having to be broken into small enough components to fit on rail cars.
I am not sure if you can implement a system that would work well when your actors are profit driven work that needs to be done can only be done exclusively by one entity at a time, and as a bonus that extra profit gives you more feedback into how the system operates. There aren't a lot of natural negative feedback to keep things under control in that system.
Especially if your goals are to reduce overhead.