So, I had an exchange with support about this. Effectively, they said "try pushing *really* hard (first 'click' may not be really latching, but keep pushing)" and miracle of miracles, it worked for the cables I had in there.
Not long after, I replaced a cable (I really only have two going in -- one from "the Internet" and the other into a 24 port switch), and did not have the same luck. No matter how hard I pushed, I couldn't get it to latch. There's something decidedly wrong with the jacks that were used on those original units. :-/