Out of curiosity, I loaded an earlier save and it worked - after some experimenting, it looks like the issue only started after I completed "The Last One." I had made a save immediately prior to that mission, and I can use that to replay missions, and another immediately after, which has the problem - both are at 100% completion, so the only difference I can see is the actual mission completion.
Very odd . . . but at least I can get my achievement again!