Hi Dan,
The Grade Me block is great for what you want. Just be aware that the last few versions seems to have various problems with assignments. The latest release, 2.8.0.3 works for grading assignments as long as you go through the Grade Me block. If you try to go grade an assignment from the normal grade view page it is hit or miss with four possible results: go to the right person, go to wrong person, and two different debug messages. I see this behavior on three different Moodle 2.8.4 sites and get the same results after upgrading to 2.8.5. I have sent an email to the maintainer about it over the weekend, but have not heard anything back yet.
I am hoping to hear from anyone else who may be trying out the latest release of Grade Me to see if they have the same problems I am seeing.
AL