I don't know if there's a way to do this in Canvas. I often suggest using Discussions for ongoing feedback, but as far as I know there is no way to limit who sees the feedback. Anyone who responds can see all the responses.
If you are a Google institution, you could combine Canvas with a Google Form. Post the assignment instructions as a Discussion in Canvas. Ask each student to use the Reply to 1) post their own paper (embedded in the RCE or as a link) and 2) provide a link to a Google Form for others to provide the feedback. Ask each student author to add the faculty members as Collaborators on their own Form so that they can see all the responses (but no other students can see them).
All students can view the Discussion with all the Replies containing their classmates' work and links to individual Forms. Each can read everyone's paper on Canvas and provide feedback using the Google Form link.