However don't you think your own explanation of improving security against accidental key reuse could be the explanation, with the repetition being there only for that purpose?
The extra protection against key reuse requires the attacker to be uncertain of which group is the indicator group. Placing indicator groups at the beginning of the broadcast would prevent that, but would allow agents to better avoid detection by minimizing the time they need to listen.
However don't you think your own explanation of improving security against accidental key reuse could be the explanation, with the repetition being there only for that purpose?