Unions do try to use cooperation. Ever heard of interest-based bargaining? ALPA loves to use it. Unfortunately, management usually isn't interested.
UAL pilots aren't mind readers. They have no way of knowing this is going on if they aren't educated.
Unlike Dubya, most people are smart enough to realize that you should exhaust all possible avenues of a peaceful solution before resorting to draconian measures. The average UAL pilot hasn't been educated on this matter yet. You should work on that before issuing threats.
That's not what you're doing. Educating doesn't come veiled in a threat or an ultimatum. Your letter should not include a threat if the intent is to educate and request assistance from the rank and file. I'm not opposed to a letter, just to the threats.