Displacer beasts could drop their hide, which can be enchanted or otherwise crafted into a cloak of displacement.

Displacer beasts may drop a hide, which can be enchanted or otherwise crafted into a cloak of displacement. (Or else this could just work with a displacer beast corpse which could be enchanted/polymorphed/crafted, without requiring a new object for the hide).

Wearing a cloak of displacement allows you to displace pets 100% of the time and also peacefuls; this still works if you are confused, stunned or hallucinating.

Bump the cloak of displacement up to MC 2.