Another thing about group work and assessment. In some courses, particularly upper-division courses with small enrollments, the same kind of individual accountability I’m looking for can be found through oral presentations, not just timed assessments.
I found this out in the textbook-free quasi-Moore Method abstract algebra course I did this past semester. Students were free to work with each other and consult outside sources on any course task they wished to, but at the end of the day their grade depended on their ability to get up in front of the class (and me) and present their work — answering questions on the particulars, being able to explain the overall strategy of a proof, and defending their work against potential holes. Students who could do this on a regular basis scored highly. Students who couldn’t scored poorly. It worked out.
And I know that the students learned a valuable lesson: You don’t present something unless you know it’s right, otherwise you’ll end up embarrassed. And don’t discount the educational value of potential embarrassment.