Best L/D and most efficient AOA

[bookworm]

I can't see any inconsistency in your original statements as they apply to a particular object. As far as I can see, the crux of your observation is:

Now you can see at level flight at speed Vmd the L/D is max. But the AOA is not the L/Dmax AOA of the aerofoil.

i.e. that the drag curve of the overall flight vehicle is not the same as the drag curve of the aerofoil in isolation. Is that surprising?