I'm not sure that your logic is correct. Have you tested this? I thought Extended Circles posts would show for anyone who was following you and who was followed within your social circles (friend of a friend). Remember that follows aren't symmetric.
Said another way, Extended Circle posts are only visible to people who your friends follow who, in turn, are following you. See this Google+ Help Article
If a person doesn't follow you, I don't believe you can inject content into their feeds.
Another difference between Public and Extended Circles is that Public posts are searchable.
Personally, I've not really found a good reason for using Extended Circles posts... maybe for a party invitation? Something you want to tell your friends and their friends about?