I don't know why some of you keep suggesting a flat spin. That makes no sense, and the evidence is stacked against that theory.
The rate of descent (ROD) in a flat spin is much less than in a regular spin - perhaps 3,000 - 4,000 fpm. For a light aircraft, a normal spin ROD is between 5,000-8,000 fpm. MSY's final descent averaged a geometric (GPS derived) ROD of 9,932 fpm - or taking altitude and time data alone, it lost 7250 ft in 44 seconds which averages out to 9,886 fpm. That is a very high rate for a spin, and I don't think possible for a flat spin.
These numbers still make me suspect there will be a critical part of an airfoil found some distance away.