I never fully solved that problem, but I found a workaround that helped: I started writing notes and drafts by hand in cursive with my non-dominant hand.
Writing by hand, by itself, calmed me and focused my mind, whereas writing in a word processor almost always caused a spiral of distraction and increasing agitation.
Increasing the difficulty of the literal, physical writing process helped me, I think, in a few ways. It became much costlier not to commit to a single version of a thought, so I had a strong incentive to pare away some of the noise surrounding it and state it in its most direct, least objectionable form.
I'm also convinced, though I can't prove it, that dramatically slowing the physical act of writing improved my working memory.
That being said, I strongly agree with just about everything this piece says, whether or not one writes by hand. And I would add that writing also forces people to use a wider range of faculties and forms of reasoning. I doubt one could overstate the value of this as intellectual exercise.