It is entirely possible that "Sick Puppy" would subscribe to a Ted Bundy sort of view about that last breath or would perhaps relish the prelude, such as repeated relaxation and re-tightening of the ligature.

However, the presence of the note and the contents of the note indicate that he also has a distinct interest in the identity of his victim. Ted Bundy would pick up any young girl with long straight hair who was willing to help a man who had his arm in a sling. Sick Puppy was not willing to kill any six year old girl he happened to encounter.
He may have selected the Ramseys for what we would consider to be an absurd reason, such as that slammed office door, but he did select his victim, not merely reach out and grab what was encountered.

I agree with your statement about attacking the weaker and I assume he was unwilling to attack John Ramsey because of a physical weakness he has or a perception of himself as too weak to tackle an adult male. Such 'weakness' might be psychological.