"How about draining Lake Pontchartrain into the Gulf, thus making New Orleans only vulnerable from the Mississippi levies, which has already been proven to withstand Katrina."
Or building a levee on the lake shore as big, or bigger, than the Mississpi levee. It will be an eyesore, and block view of the lake, but would withstand much more than the rickety and fragile system now.
It wasn't the levees along the lake itself that failed, but rather those on canals, canals essentially at the level of the Lake, designed to allow rainwater to be pumped up to lake level.
Maybe a better solution would be to eliminate those canals. Close off their axes to the lake. Then fix the levees along them to function as a compartmenting structure should the levees on the Lake itself fail.
Add a new levee to protect the area around the river from water from the Lake, including the French Quarter, Bourbon street, etc, and turn the rest of the city into a parks and recreation area.