I believe a particle's decay width/rate should depend on whether they are in matter or vacuum, but am unsure of where to find a prescription describing this phenomena. Please could someone point me in the direction of any literature on this subject? Many thanks!
A particle travelling through a plasma of particles it can interact with will indeed change its decay width. In principle the surrounding particles from the plasma will allow an initial distribution of your particle species in question to not only undergo decay processes but also be produced via the inverse decay processes. Therefore your original notion of a decay rate in vacuum will rather turn into an equilibration rate in matter/at finite temperature.
A field theoretical treatment of this subject is given e.g. in this great paper by Weldon: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.28.2007