Hey there!
Private beta sign-ups are typically distributed to groups of developers we work closely with to ensure the feature is ready before it is publicly available. As you mentioned, the Community Feedback Program is one of the groups we frequently work with.
We are working on expanding the Community Feedback Program to offer these opportunities to more developers. We have recently updated the application and are making changes as needed to be more inclusive. Feel free to send in an application here: [Open] Community Feedback Program Application!
Please note that just because the application says you do not qualify, it DOES NOT mean it will not be reviewed.
Hopefully this helps!