If submission of an assignment could be passed as a condition for completing another (dummy) assignment, then we could use the completion status of the latter to restrict access to the fomer. Unfortunately, I can't see this possible. AND I mean Moodle 2.8 ...
For Moodle 2.3, and Moodle 2.8 too, the only workaround I can think of is to adapt the quiz activity and use the essay question, forcing students to type in their texts, and to shut off all the possible review options.
In Moodle 2.8 the essay questions can be actually set up in such a way that attachments may be **required,** so there is a way to enforce submission of files. Not sure abour Moodle 2.3 here.