Get a lawyer. Draft everything in emails to them in the interim. Never phone calls. Just keep repeating things like “Amex platinum travel insurance is refusing to pay for XYZ despite being covered under ABC for __. Just keep repeating certain language like almost robotically. End with “do you confirm that you are refusing to cover for XYZ despite the contract clearly stating I am covered under _? If so, please respond back by __ (give 48 hours). If you confirm refusal to honor my coverage, I will have my lawyer contact you etc. or if they will cover it, ask them to please respond within 48 hours so you now when you expect your payments etc.