I've been reading and re-reading your post and the replies. I'm more confused than when I started! Is your concern that you are losing sight of your students' learning processes i.e. they become statistics more than people (which is what your post title implies) or is it that you are concerned about the way in which quizzes might not be the most effective vehicle for learning?
If it's the former then I might suggest you open up your course site to more interaction with students. My situation is similar to yours in terms of the student age range and teaching situation. I pepper my courses with surveys, forums etc. to make sure students are connected to the learning. Younger students go for the gradebook as you suggest. They like the idea of seeing grades "develop". Unless I need to do otherwise, all my assignments are online/upload and marked without any intervention from paper. IMHO it's about 2 to 3 times quicker, far easier to give feedback (especially on a design project where I altered the design in front of the student to show what effects I was looking for) and the feedback, being emailled out, saves class time and the negative comments that can often go with "sharing" grades in class.
Another idea I'm trialling this year is to give two senior classes different Moodle permissions to see which group takes more ownership of their work. One has the traditional role of students and the other has full teacher rights (minus gradebook editing ;) ). It'll be interesting to see what happens. Both groups are very vocal about their needs which suggests I'm on the right path. It helped that one assignment was to answer a survey - they had to tell me what they thought of their sites.
If it's the latter then the quiz link is, as you noted, very useful. If your concern is pedagogical then might you not link the various question formats in Moodle to specific outcomes for the course? This would be sound educationally/pedagogically and give variety for students. I am also trialling a spreadsheet (which should be possible in gradebook but I haven't tried it) where I record not only grades per assignment and per outcome but also assignment, class and year means and standard deviations. In addition I also calculate grade per student as an index number set against the year mean for that task and will now include the same calculation but against that students past performance (i.e. both summative and ipsative assessments). This gives the numbers yuo need for report writing, comment etc. and also a good sense of how the student is performing (students seeing how their grades work soon make the link between performance, grade and effort!.
Hope this helps,