Not sure whether there is any specific research on listening to particular songs as a reactive coping strategy for stress, but Granot et al (2021) looked at what resources people used during lockdown to help them cope and discovered that music was one of the main resources people used especially for venting negative emotions, self-connection and enjoyment. The paper is called "“Help! I Need Somebody”: Music as a Global Resource for Obtaining Wellbeing Goals in Times of Crisis" and is a really good piece of research (I think there were around 6000 participants across 11 different countries). It might be a good place to start as they may have cited research that is closer to what you are interested in? Good luck - it sounds really interesting!