I'm a little confused. I would expect this setup would work:
Parent project contains all the image sessions. None of the collaborators has any permission on the parent project.
The collaborators have their own projects with their own permissions. You share the relevant subjects + sessions into their projects. They have permissions to create the assessors in their own projects.
Does that not work?
I guess I should add this context: if you are creating these assessors using containers, what I have outlined above would not have worked until recently. As of XNAT 1.8.5 and Container Service 3.2, we have enabled containers to run on shared sessions and create assessors in the sharing-destination project.