Great! Yes, let us start with a new issue in the tracker where we can continue to discuss details. By the way, I was thinking - would "Last modified" time be useful in this table, too? So that teachers could sort the table by it and have most recently updated work at the top.
In fact, now thinking about it... Instead of having this new table as a stripped down version of the grading table from later phases - why not to have it as an additional report table focused on submissions only. It could contain more sortable columns (time modified, number of allocated assessments, grade for the submitted work etc) and it could be displayed in later phases, too. So that we would have two "reports" there - one focused on assessments (that is the table currently there) and the new one below it focused on submission details.