The solution is to let the river flood into the Marshes to the Southeast of the city as it did in the past. This will entail large tracts of development being destroyed (sorry about that Chalmette, Lousisiana). The compensation required for these areas is quite small as compared to the compensation that would be required to rebuild New Orleans.
The problem of development in areas unsuitable is also a result of idiotic policy of the Federal Government. Private insures will not issue flood insurance at a resonable rate for these areas in danger. The federal government has and as a result areas that are totally unsuitable for development have houses built on them.
The solution that nobody will accept is to let the river flood as it did in the past. You can delay the river, you can put the river in levees, that river will eventully go where it wants.