I honestly think that Brandy and Quentin could have pulled off a victory in their own layout, but Brandy's decision to assemble the Silver Monkey took away that chance. Had she gone directly into the opened Secret Password, she would have been removed immediately, giving Quentin enough time to grab the Sash and escape. If she had assembled the Silver Monkey and gone down to the Quicksand Bog, I think there would have been enough time saved for Quentin to reach the Sash, but not enough to get out.
Now onto the Empress Eugenie layout: This path was the only bottom central shaft run of Season 3 that had the team only enter one of the other central shaft rooms AND avoid the two far-left rooms of the temple. Just by necessary number of rooms entered, this run should be considered one of the easier bottom of the central shaft paths, and if any of them should have been a victory, this one was it. Janeen's hesitancy, especially in the King's Storeroom, cost this team a bit of time. Jay also had trouble in the Jesters' Court, which did not help their cause at all.
I think that Quentin and Brandy would have been victorious (or nearly victorious, i.e. Icarus) with the Empress Eugenie layout. Even though Brandy would have been removed in the Shrine of the Silver Monkey, I think Quentin would have assembled the Monkey in quick fashion. He seemed to complete his objectives competently once he composed himself in the Secret Password. Avoiding the Secret Password and Quicksand Bog altogether would have saved this team a bit of time. Also, Quentin's quick completion of the Jesters' Court would have benefited the team, since that time could have been used to escape from the temple.