I worked on the surveys and cors equipment that directly measures subsidence in Louisiana, and have worked on many of the levees and other coastal civil works.
Relocation? For a problem that hasn't happened yet and isn't likely to happen in the foreseeable future is absurd.
New York City is at a much greater risk and will be inundated long before New Orleans.
The fastest rate of subsidence in New Orleans is/was due to organics in the soil decomposing once the groundwater table was lowered (drainage projects going back 300 yrs), allowing oxygen to infiltrate. This decomposition is mostly complete in most areas of the city.
Piles under everything from skyscrapers to personal homes penetrates the organic layers, so buildings don't subside even if the ground does.
The biggest risk to the city and state is environmental activists, the EPA & the Army Corps of Engineers, and the largely untouchable Mississippi River levee system, preventing the delta land building process that counteracts subsidence by depositing new sediment in yearly floods.
Additionally, erosion/ runoff prevention and dams through out the Mississippi, Missouri, and Ohio river watersheds have decreased the amount of sediment flowing down river, and results in less sediment available for natural land building.
The coastal barrier marshes and islands are dying because we've stopped the natural processes that sustain them. Each mile of marsh results in the natural lowering of storm surge by 1/2' to 2'.
The federal government, environmental groups and others fight the restoration of these natural processes. For example, they argue fresh water introduction will hurt dolphin populations in coastal bays, but they are only capable of being there in the first place because of man made interference: the bays were freshwater until the levees cut off their natural supply of freshwater.
As for global warming? Infrastructure, business and homes are amortized at 30yrs or less. Maybe up to 50yrs for very large civil projects.
Worst case sea level rise estimates easily gives New Orleans 300+ more yrs, likely much longer, a time frame longer than the current age of the city.