I cannot speak to security groups, we have none. We manage groups externally and sync them with GCDS.
Here is how we do it.
The group to be restricted is set to all_managers_can_post
gam update group restricted.group@domain whocanpostmessage all_managers_can_post
A "broadcaster" account is assigned to the manager role of the group that needs restriction.
gam update group restricted.group@domain add manager broadcaster.account@domain
( the word user is not needed between manager and addy above )
A populated group of broadcaster delegates is assigned AS a delegate OF the manager account.
gam user broadcaster.account@domain add delegate broadcaster.delegates@domain
The broadcaster.delegates@domain group members log in as themselves, and can then open the broadcaster.account@domain mailbox as a delegate. From that tab they can send to restricted.group@domain.
We do not provide login access to the broadcaster/manager accounts; our groups are managed externally.
We have 30+ sets of these manager/delegate.groups broadcasting to ~150 groups.
Knowing what I know now, I would have done 8 orgs/sets, and cut out the suborgs.
Danny