What I ended up doing was downloading the class roster, editing out everything but the email addresses, and writing my own program to assign partners and group numbers for each assignment. Then I posted the pairings on the class's Piazza bulletin board and had students sign up for their lab groups. I only had to move about 4 students who incompetently signed up for the wrong groups (and I didn't have to find them—the students who were supposed to sign up in those groups complained).
It was still more work than a competently designed LMS would require. (I'm of the opinion that all the LMS software on the market is cobbled together by people who never took human-computer interface courses, never taught classes, and has not the slightest idea what the jobs are that the software is supposed to help with.)
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