Maintenance Plan Job running at additional unscheduled times?
Well, mystery solved.

I had previously posted this at another site (SqlServerCentral.com), and then posted here after I had not gotten a response for several hours.  While I was trying Aaron's suggestion here, a Josh posted the following there:


  Did you check the history of the job to see how it was invoked?
  Usually you'll see something like "The job succeeded. The Job was
  invoked by Schedule XXXX (Schedule_X ). The last step to run was step
  1 (XXXXXXXXXXXXXX)."
  
  Does it look the same for each run?


Though I had previously scoured the Job's history, I had not specifically looked for that message. And lo and behold, the unscheduled ones have the following:

... The Job was invoked by Alert 1.  ...


So someone must have tagged this job to run after an Alert (likely the wrong job).

Naturally now I feel silly for not checking this before.  But I post this here now, so that others in the future may benefit from my oversight.