I got a Mog!!
After some careful thinking, I swapped my team around a little. My plan was to be safe and steady over bum rushing. I also used a Time Extension for the first time. This was super helpful and I have a ton of them since I seem to only get that from that particular Daily Quest.
A'merpact was swapped for Zerro Λ. This was more of a utility swap since there is a requirement to get to Big Tonberry is seven turns. I figured this wouldn't be an issue with the Time Extension, but better safe than sorry. And with capsule eating, she was probably (slightly) more useful in dealing with the small enemies on the boss. The ice > fire element didn't seem to tilt the scales in the easier version anyway (and, read below, I ended up not fighting fire boss).
Suoh was swapped for Lunato. This was probably the key to my victory. The small enemies can be petrified (wasn't planning on that!) and Evasive Arts is ridiculously useful. Popping him back and forth between pincers made my team nearly untouchable.
Rest of team remained from Job 3 hunt (Echo, Bahl, Ma'curi, Sorman).
I overpowered the penultimate stage on accident, so I had a bad opening on the boss, primarily not being able to lock him into fire/sword. No biggie, I could use a few turns to take out the small fries. Um, then Ma'curi died. I'm not even sure how (must've looked away for a sec). Boss was now ice/bow, which was okay because I had Bahl. From here it was pretty typical, I kept him locked and chipped away. I lucked out when he summoned healer, I was not able to dispatch it right away but he didn't heal. Took it out next turn and refocused.
Overall it wasn't too bad, I managed it with two dead team members (Echo croaked, but that was probably assumed).
I mighty try to get another tomorrow. Or level Echo/Zerro up some more first. I doubt Echo will contribute much, but she's close to unlocking her last skill anyway. Zerro Λ's bomb skill is probably boss, but I don't see me getting her from 63 to 80 by the time the event ends.