Well, my here's my progress:
1. I was able to make out what was wrong with Serenity jet transparencies in the hi-res screenie I posted earlier. The cause was a bad choice of
d value in the model's
cone material. The value was less than that of jet material. But the cones are
always farther behind the jets from the observer's point of view and therefore they should be always drawn the first!
To this end, the cone's
d should be at least a tad larger than the jet's
d. See the topmost screenshot for d adjusted from 0.52 (yours) to 0.7 (mine).
2. To calc the borders that should be anti-aliased, the original FXAA shader uses, evidently for speed reasons, an approximate
luma parameter that's tied to the pixel green channel value. I changed that approximation to an exact, classic luma calc that improved the AA quality dramatically -- again practically at no GPU usage cost despite about a dozen additional square roots now being used for each screen pixel.
Default
FXAA is now almost as good as 32x MSAA with the only exception of borders whose on-screen inclination angle is very close to a multiple of 45
o except near-horizontal and near-vertical ones that are still anti-aliased all right. See the middle screenshot to compare FXAA against MSAA.
3. As I said, despite the substantial extra square root calc in the shader, the overall impact of FXAA on the GPU is close to nil. See the bottommost screenshot to compare CPU/GPU usages at 30FPS for hi-res non-AA and FXAA renders of Serenity against an animated background shader.

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The last but not the least issue I have yet to cope with, is proper mesh texture mipmapping that seems to be at fault when rendered into a non-MSAA FBO...