If you read starting here on page 8 of the previously cited thread:
http://www.antiqueradios.com/forums/...2667&start=140 , you'll find reference to increasing the value of C19, which is under the shield of the IF section. I usually find about 30 pF is enough. Increasing it more than that starts to affect the sharpness of the picture.
If you look at the schematic here:
http://www.earlytelevision.org/pdf/P...Sams-439-1.pdf , you'll see that C19 is on the anode of the video detector diode (in the 5AM8 tube).
But the above is only taking care of the faint white line, which as you point out is fairly minor compared to the horizontal bars.
If you drive the contrast and brightness too high, then you can have this effect accentuated by grid current flowing in the CRT. Backing off brightness and contrast can help. Here I should also admit that a weak CRT might make the effect worse, since you may try to drive the CRT harder by turning up the brightness, which increases the odds that the grid goes positive on the brightest parts of the picture. So DaveWM's comment may indeed be right.
Poor low frequency response in the video IF would really require an alignment to fix. If backing off the brightness and contrast makes the problem go away completely (not just lowering the contrast of the problem), then the problem is not in the video IF.
You could try increasing the value of C20 and C24. Particularly C24 you may find changes the time constant of the "recovery" from reacting to bright content in the image. Increasing it enough so that the whole screen stays uniform brightness might be more pleasing to the eye.