Scenario: I have a very large enrollment class with multiple TAs. I would like each TA to be assigned a randomly selected group of students to grade (discussions, assignments, quizzes, etc.)

As a simple example, 

• Suppose I have 90 students and 3 TAs
• Students are assigned a graded discussion with a rubric. 
• I would like to have the following:
  • TA 1: Grades the discussion for 30 students.
  • TA 2: Grades the discussion for a different 30 students.
  • TA 3: Grades the discussion for the remaining 30 students.

Tried Solutions that Did Not Work:

1. Moderated Grading. This tool doesn't apply to my situation. I do not want to have multiple graders grade one student (i.e., which is what moderated grading does). I want to divvy up the responsibility of grading one assignment to multiple graders.
2. Just have TAs grade their assigned groups. I would normally assign different groups to different TAs for grading ("TA 1, you are in charge of groups 1, 2,..."). However, my dive into this community has taught me that using multiple graders is a no-no on a single assignment: "SpeedGrader is generally designed for one instructor role to grade submissions at a time. Because of how SpeedGrader data is loaded and stored in the browser, multiple users should not grade assignments at the same time since each grader cannot view the most recent information for a submission."
3. Create sections. This was hopeful but my institution doesn't allow it. I have no ability to create sections for my course. 

Any ideas?