An awful situation indeed. Seems quite cut and dried, in fact.
There must be ways to continue to pursue this and get to higher management. I think it's time for you to return to the telephone route, sir. Alternatively, in Boston, there is a lawyer, Mr. Daniel Yanofsky, who is excellent. His contact information is online and he has a wealth of corporate experience. False advertising is an egregious act.
RE: American Airlines misrepresented baggage policy on award booking containing an Alaska Airlines segment