If the frame is correctly exposed except for a lighter band, that may indicate an overlap, which might happen if the shutter is delayed in its travel. HSS fires the flash with extremely precise timing in order to make the band produced by the shutter slit at each flash exactly join to the next -- but if the shutter travels faster than the camera's computer expects, you'll get dark band(s) where part of the sensor didn't receive light from the flash, and if the shutter moves slower than expected, you'll get light bands where the flash lighting overlapped on the sensor.
In your case, if you're getting a single light band at 1000 and the same at 4000, it's clear the shutter isn't traveling slow for the whole frame (that would produce multiple bright bands at shutter slit width apart); rather, it's hanging on something at one point.
If your camera body has enough value, it may be possible to have it repaired -- this might be simply due to a foreign object lodged in the shutter's guide groove, or a bent leaf (I'm presuming it's a metal shutter; I've never heard of a cloth one that can shoot at 4000). It might be possible to repair the shutter for less than the replacement value of the body -- or it might not, if the body is more than a couple years old.