Issue
You want to re-deploy the same commit SHA from a private GitHub repo.
Resolution
This can be done with the builds-create
Platform API endpoint
https://devcenter.heroku.com/articles/platform-api-reference#build-create
There is a Builds CLI plugin that makes this easier:
heroku builds:create --source-url https://api.github.com/repos/<username>/<repo>/tarball/<branch>?access_token=<github-personal-access-token> --app <app-name>