Normally, HSS means the pulses should come so often that as the slit moves over the sensor, each part of the sensor sees multiple pulses before the slit have moved too far.
If HSS is using 50kHz pulse frequency, and the camera has 1/4000 shutter speed, and the actual travel speed of the shutter curtain is 1/250, then the slit width would be 250/4000 = 1/16 of the sensor and there would be 50000/250 = 200 pulses during the full travel of the slit. So the slit width should be big enough for about 12 pulses, i.e. each pulse (seen or not) should represent about 10% of the light seen by the individual sensor pixels. At 1/8000, there would be time for about 6 pulses hitting individual sensor pixels while the slit moves over the sensor.
I really can't understand why there are these narrow bands seen, unless there is some interference there meaning the sensor sees 11, 12, 11, 12, 11, 12, 11, 12 pulses.