A flat fee of $10K for an appeal?

Here's one for all the appellate nerds out there....
Client retains Attorney to do two appeals, one for a flat fee of $10K, another for $20K. So what happens? Attorney prepares (allegedly) "incomplete and incompetent" briefs that the Court of Appeal rejects. (Shocker!) Even though Client has to retain new appellate counsel to file the briefs, Attorney refuses to return Client's retainers. Client then sues Attorney for breach of contract and money had and received. (Obviously.) A bench trial is held, but is unreported. (Sidelight: Client's expert witness is an appellate lawyer with decades of experience, but is not a certified specialist. Attorney attacks the witness on that basis. Held: "Meritless" nonsense.) Client wins. Attorney appeals. Judgment affirmed for failure to provide an adequate record. (Yep.)

They don't meet, do they?