My advice would be to keep it simple and not try to interact with google. If necessary, register another domain in the same account and set up spf, dmarc, dkim and send from that, to your destination - don’t publish that email address anywhere. If you ever manage to send from an email address that is in any way linked to google please do let me know how you did it. I’ve done exactly what I’ve just described and found it to be the only way that works.