IMO both the killer and Karr have a problem with authority figures......Out manipulating them, out smarting them. Karr's controlling issues with his spouses and his being "too strict" in the classroom would also be part of this pattern.
Karr signs the yearbook, perhaps someday I Shall Be The Conqueror! The ransom note is signed, Victory! S.B.T.C. In tandem with what you said...