What about having an admin user management screen similar to the JIRA user project role?

This will help to administer who has access to a space with what permission.

The rows would indicate the spaces, the columns would indicate the space permissions.

If a permission to space is provided via a group then it is displayed with a group icon.
If a permission to space is provided to the user directly then it is displayed with a user icon.
if the permission was not granted for the space then it is displayed with a red cross.