Using a GitHub app AND a variable for URL (Reusing a VCS Root)

We have a common VCS root.  Each application uses the same one, then they pass in a variable to the “Fetch URL” to have their code pulled.  This is working great in BitBucket.  

We are now moving to GitHub, and I do not want to use a “user” to get the code. (GitHub charges $30 per user per month.)  I want to use a GitHub App.  But I can't seem to find a way to have the “common VCS root” pattern work.  When I put in the “Refreshable Access Token” option, and then press “Generate Token” it needs me to select a repository.  We have hundreds of repositories with more being added all the time.  I really do not want to have to manage a list of repositories here.

Is there a way to use a GitHub App that has been scoped to all repos in the GitHub Organization to just allow it to pull from all repos?