I don't think CMJA is dictating appeals strategy, though I'm sure she believes she'd be better at it than her appointed attorneys.
My latest uneducated guess about what's going on comes from reading a US Court of Appeals ruling on an habeus corpus appeal by Richard Glossip (on Oklahoma death row, execution just delayed by 2 weeks).
It's a really good read, BTW, for anyone interested in how appeals relating to ineffective counsel, etc. are heard, discussed, and ruled upon at the federal level... here's the link:
www.ca10.uscourts.gov/opinions/10/10-6244.pdf
(edited link-sorry. Had posted wrong link).
My take away of relevance here (if I understood correctly) is the Court's insistence that it could not take into consideration any claims of constitutional violations that had not been raised during the state- level appeals process.
Hmm. Based on that, my guess is that her AA doesn't anticipate actually being able to disqualify the COA altogether, and perhaps, not even the 3 judges who ruled against CMJA's Special Action. Perhaps the AA is just trying to fashion a constitutional violations argument related to the COA's role, and entered the related motion to disqualify to ensure the issues were included in the state-level appellate record.
I got so wrapped up in the case being appealed in your link (Glossip) I forgot to apply any of it to JA's case. lol Also (on another case), I much appreciate your views and knowledge shared on the Viafore thread, I've been following it since near the beginning and am in complete agreement, esp. after having viewed some of the LE interview in the 48 Hrs. program.