I have a feeling that a lot of the work that shows up on the Random Read is a bit old and perhaps the writer isn't interested in any more feedback. How about including a box when a writer uploads a piece of work which he ticks if he/she wants their work to appear on the Random Read? They could untick the box when they don't want any more comments. Then if anyone feels like commenting, there's a place to go to usefully choose a piece to comment on. It might encourage people to comment outside their group.
What do you think?

I don't think that I've ever read a Random Read - there is so much other material to keep up with, along with work work and writing that it has never occurred to me to look for this part of the site.

It may be that I am missing something.

Sorry not an answer to your question.

BB, I think that for a lot of people the RR is a bit redundant. I made this suggestion to try and make it more useful. Some people don't crit at all, others are fully occupied with their groups but occasionally people have time and are willing to crit something new and this might give them a good place to dip into if it was organised differently.