I think I've found a solution. I don't know if it's the best solution, but it does appear to be a solution.
Place the playhead in the gap. Select all strips to the right. This won't select the audio overlay because it doesn't start to the right of the playhead, but it will select everything else. Then Grab, and manually move left so it overlaps the strips to the left of the gap. On confirmation, the two strips to the right will have been moved so that there's no gap, and every other strip will have been removed the appropriate amount.
If, however, I come back in ten minutes discovering that everything's been garbled because all my carefully placed overlays and crossfades have been rearranged, I will scream here, and you'll know it didn't actually work.