But when working with people in the normal job, nobody is watching them type they just eat the sausage.
I can relate. I don’t have anxiety generally with work and have been praised on my interactions with customers. But I feel anxious during interviews because they are actively trying to judge me.
Then again, maybe I'm biased because I write the same sentence multiple times in quick succession. And I go back and re-write previous sentences if they don't flow well with what's coming next. But when people have watched me do it, they have only expressed wonder and admiration over it, never negative feelings.
What doesn't work is when someone starts verbally editing my first draft the instant I've typed it out. Yes, I know it's bad -- it's the first draft. I just needed to get something on the page to see where I should go next.
I would imagine that, if anything, seeing you pause after an initial draft, adjust some grammar and tone, pause...even re-write a sentence or paragraph - and then say "done"...would impress, not detract.
As far as your technique, drafting then editing down is a totally legit way to write. I wish more people did that!
Adaptation only goes so far. More training won't turn a dwarf into a basketball centre, or a heavyweight bodybuilder into a champion marathoner. Sometimes you've got to work with what you have, both in terms of abilities and limitations.
Intellectual and psychological limitations may be less manifestly visible but are no less real.
Just like if you're nervous about driving on the freeway, or flying in an airplane.
Heck, I remember buying my first phone answering machine. I froze up repeatedly trying to record the message. After a while, that problem went away.