A Stancor A-8130 "universal" flyback is on the way. While skimming a Wallace Telaide for Zenith 1947-1953, I came across this section on Barkhausen oscillation. I think I'll try suggestion 5 if the new flyback doesn't work any better.
This oscillation usually appears on the picture tube screen as one or several dark vertical lines and is most prevalent under weak signal conditions. One of the following suggestions can be used to correct the condition:
1. Turn the Horizontal Drive Control to a point where the lines disappear. The Width Control should then be adjusted to obtain proper width.
2. Replace the 6BG6G horizontal output tube. It must be noted that a tube which produces a Barkhausen oscillation in one receiver may be entirely satisfactory in another.
3. Mount and adjust a small magnet on the 6BG6G tube until the oscillation is removed.
4. In some early receivers, the 6BG6G cathode was by-passed with a 40 Mid electrolytic capacitor. Remove the cathode lead from this capacitor and connect it to the 20 Mid unused capacitor which is directly adjacent to the 40 Mid unit.
5. Try a different value by-pass capacitor in the screen circuit of the 6BG6G horizontal output tube. A value of .001 or .002 Mid usually will be found satisfactory.