I'm not sure if this solution meets all your needs, but a simple solution might be simply to set each task up as an assignment (either a file upload or online text would be my suggestion, but this might vary according to the task) with a grading scheme that could include something like: A-Supervisor, B-supervisor, C-supervisor, A-assessor, B-assessor, C-assessor - or some other such system to show whether the task has been graded by the local supervisor or yourself as the ultimate assessor. The feedback section can also be used where you establish a protocol for the supervisors/assessor to use different colours e.g. red for supervisor, green for assessor.
If you allow reuploading and no deadlines, then students can go back and redo tasks as necessary.
The grading overview reports would then give you an overview of who has completed what and who it has been assessed by.
This is just an initial thought based on my limited knowledge of the assessment system built in to Moodle and without any of the possible plugins that may be of further use and can possibly be refined or replaced by anyone who has done anything like this themselves