Here is an updated circle for you to use to share your private videos with. In order for this type of sharing to work, you will have to add this to your Page’s circles, however.
To do this, switch over to your page in google plus by clicking on your picture in the top right and then selecting your page. Then, navigate to this community (search for it in the box at the top is the easiest way) and click on Add People from this post.
Let me know if that doesn’t make sense.