Graham, it's funny that you should have this problem.
Last week someone sent me a file with the exact same issue. He had a bazillion groups within groups and another couple of sets of control groups.
As you said, the options for UnGroup and/or Ctrl+K (break apart) were greyed out.
After I hollered at him for getting himself into such a mess (Yikes!)...............I have no idea how he got to that point, the only thing that I could do was the following:
Please try it for me and let me know if it helps you, too.
[1] Select one of those Control Groups of ??? objects.
[2] Nudge it slightlly with one of the arrow keys on your keyboard.
[3] Does the Status Bar now change to a plain old Group?
I don't know what kind of 'control' you used for your group. In his case, it was a contour group.
As soon as I nudged it a little, the Ctrl+K option became available.
(If you nudge the Control group just one click, you can immediately nudge it back the same one click...........and you should still be fine. Your file will stay in tact and not be altered.)
Let me know.
I'm anxious to see if that will work for you as well.