What a coincidence, I just finished watching this video on youtube. Although your slightly better geared than me (based on your hp, im sitting on 7.8k), I saw a couple things you could do to make it go faster.

Threat didnt seem to be a issue for you even with your BLM spamming Flare. So use Steel Cyclone when you can. What I like to do for all group after first boss is pop Foresight, Convalescene, Feather Foot Right before I gather them together. Overpower 2x > Prepped Wrath Steel Cyclone > Infuriate > Steel Cyclone > Vengeance> Overpower > BBcombo > Overpower > BBcombo> Steel Cyclone. If your party is doing it right, the mobs should be dead b4 you get to your 3rd Steel Cyclone, which could use for the next fight.

Also I dont think i saw you use Bloodbath which works very well with Overpower and Steel Cyclone. The HP recovered might seem minor but it can recover 300-600+ hp per Overpower/SteelCyclone because of mob mutiplier.