I admit I did not read all the above conversation, but @jzychik are you sure you need this to be at staging.domain.com? For close to zero effort you can get a preview deployment of every pull request you create at your githup repo.
It will have a complicated name like https://deploy-preview-6--angry-tereshkova-959566.netlify.com (a preview deploy for http://sonomamatsuri.com/)
See :