Margins of error aren't that bad. A kind of triangulation method would work. As a simplified example:
person A believes they got 92-96 / 120
person B believes they got 96-100 / 120
Say bboth person A and person B end up with 90. From that you can make a reasonably accurate assumption that 96 was the band 6 cutoff.
Once you collect all the data I think you will get within the cutoffs +- 1 mark. Good idea