Rashi does note that the Kohen ha'gadon should have prayed that there be no accidental murders. But I'm wondering if anyone has heard of a more direct relationship between the life of the murderer and death of the kohen.
(What vaguely comes to mind is the passing of Aharon ha'Kohen (ha'gadol) in the beginning of Parashat Masei... perhaps his love for life, for others, and his potential willingness to sacrifice his life for others. But not sure what about the essence of kohanim and murderers.)