I approach post-docs within the uni and academics from other universities to comment on my written work. That's because the sun doesn't always shine from my sups *&^%. What do you do?
Could you ask a PhD friend? Asking other people you don't know to read it is a big favour... But then I would think that because I am quite shy and rubbish at exploiting the 'research network'!! Personally I would depend on my Sup if I was new to it all. Otherwise I would just send it off as it is and see what happens!
Oops! forgot to mention that he's a professor in theology and religious study from another uni. Met him at a conference ages ago. I've always believed that when you ask, it may be given. Alternatively, he could have said NO.
I try to explain what I do to others who are not involved. If I manage to get them interested and if they understand what I do: I know I am doing a good job.
If I loose them, I ask what the problem issue is and see whether I need to work on that.
Feedback on written work is different from talking about it. Writing is a skill which is sorely lacking in me. Its just so HARRRRRD! But I do believe that practise makes perfect. Just have to keep at it.