Glad to see some rejuvenation of this discussion, aelephant. I was beginning to think that there was nobody out there interested in Stoicism and other philosophical issues! A lot of this blog and forum are about our physical capabilities, but I'm equally if not more interested in how we can modify our attitudes and reactions to make ourselves stronger and more resilient. And I think Stoics had a lot to say about this.
I do agree with you that we should pay attention to negative emotions because they are "telling us something" like a canary in a coal mine. We should definitely not ignore them. But what exactly are these emotions telling us? Are they telling us more about events and other people, or are they telling us about how we react to those events and people? Consider a single event: your car gets a flat tire on the highway. Some people will calmly realize the problem and fix the tire themselves or call road service. Others will freak out, become upset, start swearing and maybe even blaming other people for the problem. Do these negative emotions add anything or make us better able to deal with the situation? What the Stoics realized is that negative emotions are largely self-generated and conditioned, and frequently go well beyond being a "signal" about a problem, to actually getting in the way of solving problems and living life. So I don't see that we actually need to have negative emotions to get us to recognize the existence of problems. I feel I that I fully recognize many "problems" every day without feeling bad about them. Sometimes problems even energize me to feel good about helping to solve or overcome them.
I re-read Part 2 of Irvine's series, from which you took the quote about people being the source of most negative emotions. I agree with you that his statement, as it is written, is definitely not true. It is not literally true that other people cause our negative emotions. But in the context of the whole article, I think what Irvine meant to say, and could have said more accurately, is that many or most of our negative emotions are caused by the way we react to other people. These emotions are not literally caused by other people, which can be proven by the fact that different individuals will respond differently to the actions of other people. If you look at his concept of "insult pacificism", he is agreeing with the Stoics that it is not the insult, but our reaction to it, that generates negative emotions.
I think the key insight of the Stoics was in realizing that negative emotions are optional. They are largely conditioned in a Pavlovian sense, and may seem "automatized" in the moment, but through reflection and training we can actually moderate and change the way we respond to external events, just as we can we change the way we respond to food. Once I realized that (a) our reponses to events and people are conditioned and can be changed; and (b) a negative emotional response is rarely helpful in and of itself, that helped me to realize there was little value in getting frustrated, angry or sad about things.
While I think that most reactive negative emotions are not helpful at all in any practical way, I do differ with the Stoics on on particular type of negative emotion, the type that dignifies us as human beings: the sadness, wistfulness or longing we feel on losing a loved one, recalling a fond memory or hearing a certain piece of music; the indignity and hurt that comes from seeing a true injustice (rather than a minor personal insult), or other emotions that "make us human". But I see these as being in a different class entirely than being quick to anger, easily frustrated, or crying at the drop of a hat.