As far as I can tell, applying emotional intelligence is akin to using a rudder; it doesn’t correct your heading all at once, but it does start aligning you with your goals.
So for negative emotions, I try to jump straight to apathy or boredom (oh well, it is what it is, we all die anyway) but if I can’t do that, I abide in whatever state gives me the feeling of relief, until it no longer relieves me and feels uncomfortable, then I move to the next state where I feel relief again. (Anger relieves my depression, frustration relieves my anger, pessimism relieves my frustration, etc.) Once I’m at boredom or apathy, I abide and chill until it opens into mild satisfaction (things aren’t going to plan, but at least I’ve got some tasty food or an entertaining video), and from there I naturally rise into optimism, hope, excitement, and joy.
In my experience, it’s easy to navigate the positive (just milk the crap out of it), but it requires some finesse and awareness to navigate the negative.