Yeah, very good point. Rational thinking while being in a hyper emotional state is extremely tough. I think the trick is not to rationalize every thought and emotions but rather to reach an overall state of "acceptance" that emotions can be "irrational". This is more of a practice in meditation or in stoicism that slowly gives us an ability to make rational choices while acknowledging that what we are feeling right now transcends logic and reason and the futility of having a discussion with it or indulging in it in an investigative sort of way. For example: a stoic asks himself if the anger that he is feeling adds any value to the situation at hand. He reminds himself that this rush of emotions impairs his ability to makes rational choices and it is stupid to let it control you so much. Just this reminder to yourself every time you feel anger weakens it over time.

I don't like to view emotions and rational thinking as if they are somehow opposite to each other or as if doing one means we are suppressing the other I think they are really interrelated to each other. Our thoughts directly influence our emotions, like you can literally think yourself to a bad mood. So I believe rational thinking plays an important role in "sorting" our emotions. I agree that emotions are "non-instaneous" and hence takes some time to manifest. That's why I think rational thinking may not instantaneously fix our mood but if practiced as a habit allows us to have greater control over our emotions over time.

I am not sure how well this approach works. I currently live in India and I notice that a lot of emotionally suffering and depressed folks are those that have a comfortable, financially well off setup (perhaps too well off). On the other hand, I also get to interact with labourers and poor people. Somehow most of those folks seem quite content and peaceful with their life (as long as they are able manage day to day survival). So I don't think physical or material suffering equate mental suffering although they may be a driver. Perhaps the poor don't live as complicated a life as the rich folks and perhaps they don't have the luxury or patience to go through existential crisis like the rich folks.