Here is what i figured out to be best if you have to do first\second and fifth\sixth cage sets as a WAR.

For first set, i use my berserk around 1 sec before the pull, that way i can get 2 FC, 2 combos and fracture in, not perfect, but what can you do. If you ll have to do second cage berserk will be of CD when you go in, for first it ll be on CD, but you ll have around 10 second of berserk, enough to setup 5 stacks and get 2 FC in zerk.

You ll never do 3th\4th purple cage as WAR since it happens at the same time as white cage, so feel free to setup berserks as you wish on those ones.

For 5th\6th cage i play absolutely safe, and start saving my berserk from around second cat phase. This far into the fight i dont really care about my DPS, since my group knows if we execute all mech's properly we wont get an enrage.