It's a nice conspiracy theory, but have you considered that maybe, just maybe. Chevron should be overruled not because of any back room dealing but because there's been a mountain of evidence that it was a mistake in the first place failing on its own right?
All of this side drama is kind of pointless when we can see the arguments for and against here in public and judge them ourselves.
The drama is distraction from the reasonable arguments that really matter in Court decisions.