With the way these multi-trillion dollar companies operate today and how the support staff act like corporate drones, I have no hope that attaching PGP signatures would lead to any different outcome. The response from the support would probably be going to like, "PGP what?"
I don't think any more human interaction was involved than a very bored and harried call center employee clicking 'confirm' on a bot-generated response here. You can have all the cryptographic proof you want, but you're screaming into the void.