Her current attorneys are definitely competent; one of them actually won an important constitutional case in the ASC. This team did replace another public defender appellate atty (Henny Martin or some such) , but I don't remember hearing about why the original atty was replaced/left.
I imagine the killer won't have any influence about what goes into the actual appeal brief, and I'm sure that brief is all that matters. This insult- the- COA sideshow sure seems to be her product --ugly, vengeful, a vastly over- inflated sense of self-importance, and a certainty that ordinary rules don't apply to her own grand self.
LinTX is right, of course. To the COA and ASC she'll be just one more not terribly interesting case to dispose of forthwith.