I wouldn't take this approach, until after consulting with an attorney and concluding that it is worth the time and expense. Once you mention this possibility to a large company it is likely the file will be forwarded to their legal department, and the character of the discussion becomes adversarial.
Correct here. I worked for a company years ago where any threatening of legal action (even "you'll be hearing from my lawyer!") required us to hand the customer a card with our counsel's information on it and say that any and all additional discussions must be handled through them and a notation made on the account for anyone else they contact to repeat the same.