Upside down ("Dinnerbone" / "Grumm") parrots not upside down as ShoulderEntity

Not sure if this is intended or simply not possible as ShoulderEntity, but if you name parrots e.g. "Dinnerbone" to have them upside down, they are upside down as entity, but not as ShoulderEntity.

I fiddled with their texture and would find it helpful for mapmakers if they could also be upside down on your shoulder to make use of them retextured.

Considering a player can mount on upside-down horses and pigs, this seems not to be intended (unless not possible code-wise).