Peergrade.io might be the better way. With Peergrade, students submit their assignments electronically, then the site distributes them out for peer grading for you. Student evaluators use your rubric to assess the essay. The essays are then returned to the authors with the the student feedback.
What makes Peergrade sound so promising is the teacher reports that it generates. You can find out whether students are grading the papers they are responsible for, and using an internal algorithm it tells you whether some students are grading too easy or too harshly. What makes Peergrade so cool is that it is not limited to text files. Sure, students can submit .doc and .pdf files, but they can also submit images (like with .jpg files), audio files (like with .mp3), and video (like with YouTube videos and .mov files).
One issue of concern: Peergrade is free but only for classes of up to 20 students. Above that and a fee structure kicks in.
Peergrade doesn't have video tutorials yet but click here for its FAQs.