Um, wow, you seem to have covered it all.

I agree with Teatime being a much scarier character than Carcer, they were both psychotic and clever, but Teatime actually considered it. He planned his acts, whereas Carcer seemed to live more in the moment - he had some planning (i.e. lots of knives), but the fact that Teatime would actually sit down and think about how he would kill the Hogfather and Death is a whole different level.

(Playing blind Pictionary, me drawing)
Ella: Is it a giraffe?
Me (stops drawing): No
Ella: Star Trek?
Me: Yes!