Traffic analysis might be enough to expose the structure of covert organizations.
What if 20% of the members of the organization have a daily task to make sure they create and send a total of at least 10 to 20 encrypted messages each at random times of day? The actual 20% of org members who have this task would rotate daily, And most members of the org have no knowledge or assignment other than to create and send the messages.
A random number between 0 and 50% of the total messages are sent to actual other members of the organization which can be anyone, so the structure of the org is hidden.
The rest of the messages are sent to strangers' valid phone numbers learned from other sources. In other words; the organization has a daily task of members sending encrypted messages to outsiders who cannot even decrypt the message. Since the phone numbers are random; an adversary looking in cannot tell whether the message is readable by the recipient, or if the message is Spam as far as the recipient is concerned.
The message has to be decrypted by an initial layer first before the recipient can tell whether it even claims to be a legitimate message.
When a member of the organization receives such a message they are to flip a coin and pick between ignoring the message or giving a canned reply based on their own study of how people react to receiving a message from a stranger they don't understand.