I forgot to mention that in my first attempt I had the nearest LOD--like the now two father LODs--utilize blending (tfBlend 1). This looks nicer as long as the line of sight is not from a particularly low perspective and so does not have the grass superimposed against some other object and the distant terrain/skyline. When that happens, the really odd effect of partly seeing through the object occurs, making it look ghostly where the grass is seen against it.
And so I made tfBlend 0 so that this weirdness will not occur. This is crucially important for any viewpoint near the ground, as when sitting in a low cockpit, for example, and for folk who like to build detailed scenery to be seen from the on-the-ground perspective. The disadvantage is a somewhat 'harder' appearance for the edges of the grass, and a generally more 'full' appearance.
One thing that is not satisfactory is the way the grass largely disappears when seen from directly overhead, made more noticeable on rather darker ground. I may place a single, horizontal, variegated, semi-transparent texture of almost equal lightness of tone that sits barely above the ground. This would go some ways toward diminishing the 'disappearing grass' phenomenon when it sits on a darker landscape texture.