Funny enough, now I tested with another profile and got similar results to yours, despite I made dozens of tests with other sources as well and never got convincing results, more sharpening instead of blurring or as you say many faint halo repetitions halo^n :S
For getting the samples I used in a stable scene:
temporalsoften(10,255,255)
blur(1.58,0) # since here halo is vertical
input:21,41,147,217,227,223,216,188,179,189
desired output:21,41,147,189
matrix: -3 10 4 -4 8 -6 100 -6 8 -4 4 10 -3
My thinking is its better to find a sample nearer to black as a base point, I think that's where I failed getting 71 as a base value.
I then used the contrasharpened dehalo you suggested (thanks a lot for this one)
and finally mcawarpsharp(4,4) for removing remaining halo and sharpening contours a bit.
In this case I will downscale everything a bit so look will be more compact.
http://screenshotcomparison.com/comparison/94353
From here I could do better with more fine tweaking, masking, etc sorry for disturbing again, now I guess I don't need to uninstall octave : D