Hi Louise,
The process you describe is just what we use here at Moore College. We had a custom assignment type for Moodle 1.9, which we updated for 2.1 and 2.2, that offers that plus Blind Marking (in this case, only seeing the student UserIDs, which are their student numbers). It still works as an "Assignment (2.2)" in Moodle 2.4 (which has Blind Marking built in) but doesn't allow the controlled release of feedback (as far as I can tell). If I can figure out how to put in a feature request, I'll let you know and you can "vote it up"
Cheers,
Rob