As it turned out, the truth presented itself to me readily, though I wasn't totally thrilled to realize it.
This is all a convoluted form of roleplaying.
I admit it; I have a bit of a bias against the label of "RP." This is mostly because there's so much bad roleplaying out there, and, writing snob that I am, it drives me crazy to see poor characterizations and structure. I know it's not all bad, but that doesn't stop the bias from pinging around my head. Forgive me, dedicated RPers who have some actual ability and talent.
Though our pets and our hunters are a part of us, they have their own personalities, some of which evolve without our direct involvement or control. That's just good writing. The characters take over and develop organically. For a character to truly be "real," it needs to detach itself from its creator in that sort of way. It's the pinnacle of what I consider to be proper character creation - complete separation from the subject, despite it still being part of you.
And this is why I take my pets' personalities so seriously. They speak to me in their own voices (though not always with words), something that not all characters born of my mind or heart do. Not all of them, of course; just the ones that are well-defined.
They are definitely the ones in charge here. And that is completely fine by me.