Your analysis of Spike's characterization is spot on, both in everything about his feelings and its level of villainy. It really isn't so much of a villain song so much as a song utilizing a villain, but still felt appropriate to throw in here. I'm sure you already know that the other song I nominated from the episode was the real villain of the hour.
Though I would note, in comparison to most of the songs from the episode, Rest In Peace does have a more villainous tinge to it. It just wouldn't stand out for that reason in a sea of villain songs!
The batman villians all seem to be one big joke that batman refuses to laugh at - SantaRPG