I'm also going to chime in and agree that Bardem's and Ala Mhigo both have some pretty large damage bumps when groups are being stacked together. This is especially true in Bardem if a tank is still running in i270 gear. It's a small ilvl jump but the defense bonuses the tank gain for being at capped ilvl is immense.

In fact, if you want to put into perspective the leaps in Defense / MDefense values that higher ilvl gear has, go to the market board and look at jumps in Def / MDef value on tank gear after i270. This should emphasize both the importance of a tank to update their gear and also show you how much of a difference the seemingly small leap in ilvl means to helping you keep your tank alive.

Ala Mhigo is also a culprit to mass pulls because the instance itself caps at ilvl 310. This means tanks feeling invincible due to no ilvl sync (yet) in Kugane / Temple of Fist / Scylla won't have the same benefits in Ala Mhigo. I also think ilvl sync also removes the bonuses given by Materia, which can also affect tank survability if they have a lot Tenacity melded. This is coupled with some trash having some pretty potent tank busters *Glares at gorillas and motorcycles* leads to some pretty crazy damage spikes that may be hard to heal if you aren't ilvl capped.

In essence, don't feel too bad if things go pretty far south in these two dungeons. If a tank can't gauge the limitations of the party and goes wall-to-wall, there might not be anything you can do about that as a healer and unfortunately, there's not much you can do about it at that point.