Bearfoil, it's time for another thought experiment.
Note that at a typical falling object's terminal velocity, about120 MPH, hitting water is pretty close to hitting a farmer's field. Both are effectively a solid immovable object. The land and the water cannot get out of the way of the moving object fast enough to appear materially different from a perfect solid.
With that in mind hitting the water at a small angle with a mostly downward and somewhat forward velocity vector with a small rotational component about at least the plane's Z axis. Mostly downwards and "typical terminal velocity" means the plane does not so much cut the water as it flattens out on the water.
I'm not sure if that's what you meant by the flat plate. A pure flat plate will behave much like a playing card in a hurricane. (grin - feel free to experiment {^_-}) It's not likely to land flat. A plane's configuration, on the other paw, seems to make a more or less flat encounter with a surface far enough below one of the two stable states, as I understand it. Pure nose down may be stable or merely meta-stable. I don't know. It works for bombs, though. But they don't have wings designed to make the bombs (metaphorically speaking) want to fly. Planes do. So for a plane the horizontal plane is one of its most likely orientations, even when falling. Graybeard posted an excellent example,
lost plane, punch out, followed by a long flat furrow in a farmer's field and an F-106 that flew again.
So as I see it I am not boggled at the plane hitting nearly flat despite all the WW-II spin videos out there on the web. Nor am I boggled by the concept that it was not spinning at all fast. The VS is still there to prevent a rapid spin. But, for one reason or another the plane lost enough forward velocity that it lost engines (at least for a minute or so). That could lead to a sink out of which they had no escape. Or, the transmission gap may mean no engines, recover, too low, plane encounters water and it's all over. (I suspect that if they were conscious the pilots did not see the water until it was thoroughly too late - dark, stormy, rain, ground? What ground?