Given that going viral on Twitter is the only functional help desk for such situations, “Tweet storm as a service” would be a promising proposition.
It might not do anything - writing a letter that sufficiently implies that you are actually collecting documentation and preparing for a lawsuit is an actual skill, and your demands may be unreasonable for them to handle - but you will get an actual factual human being to at least start reading what you've written. And as a bonus, their KPI is in terms of "number of incidents per year" rather than "number of resolved tickets per day".
I've had better luck lately just using contact services to find the personal cellphone and email address of high-ranking employees and contacting them to get escalation.