I'm happier with the plying on this skein.
I'm using a slightly different approach and it is resulting in more even plying through the thick sections. This time I held the two strands being plied in opposite hands. I originally started off trying to keep the thick and thin strand tensioned while holding the thin thread loosely and allowing it to wrap/ply, but I hadn't gone far when I discovered it worked better for me doing it the other way. So after a bit of experimenting I held the thin black thread fairly taut and let the softly spun thick and thin strand do the wrapping/ply. I found I was better able to control the rate of plying through the thick areas this way.
Now I just need more practice. And that will require more of a resource I seem to be in terribly short supply of lately --- TIME!