The short answer is 'it depends'.
But frankly, the Eyrie player sounds like the problem, as the Eyrie must attack every turn if it ever wants to attack (or has the commander as its leader)so should be the primary Cat stopper. Have the best puzzle player/aggressive strategy player take the Eyrie.
Next, the Vagabond player needs to maximize his vps. This alone should put a clock on everyone else as left alone, the Vagabond will win with a competent player.
Third, the WA is one of if not the most powerful faction in the game once everyone knows the game. Get your first base out asap for +card draw, then strategiclly place the rest to blow up your enemies, finally drop favor cards and organized sympathy for massive come from behind wins.
I still dont recall every seeing the Cat win on vps. Up until recently, it was the only only faction I had not won with, and only this weekend won a dominance victory with them. Your group problem is still simply player inexperience, so take the above into mind with your next game.
Thank you. Probably the best advice someone has offered so far on this thread