Assuming you're using 2 schs, whichever sch missed the stun on Barolithic Shell should immediately start dispelling as well. You can get 2-3 Dispels in before your next stun rotation is up, usually. Along with brds and rdm, all of the buffs should be gone pretty quick.
Sch's don't need Embrava or Marches, though those certainly make stunning a lot more convenient. Alacrity along with simple Haste is enough to keep up with moves, between two sch's. Pyroclastic Surge isn't any big deal, and Tyrranical Blow shouldn't be too bad, but anything else should definitely be stunned.
Peiste: Don't stun everything. Focus everything on stunning Calcifying Mist. Since it can use another TP move immediately after being stunned, there's a chance of multiple Calcifying Mists being used in a row. Stunners need to be ready for that. Divine Caress+Accession+Paralyna after Torpefying Charge, and the rest should be trivial damage that you can cover with curagas.
Kurma: It's almost impossible to stun Harden Shell, and impossible (outside random luck) to stun Tortoise Song, so stunners can just free stun after any given move to give an extra couple seconds to the whm for healing. Don't think you want to actually stun most the moves, since they increase the damage of the DDs. Stun Tetsudo Tremor, of course.
It always seems to me that if anything's going to go wrong, it's going to happen in the first 10-20 seconds. Perhaps the whms were in a curaga mindset, and in the initial pull one DD took a lot of damage before being positioned with everyone else, so they go down to an AOE. Sleepga or Breakga happening as it runs in can also be a problem, as is any major TP move that happens before it gets into range of the stunners (one stunner should be up near the melee during the initial pull to catch stuff like that).
I'm still not sure what exactly happens in those first few seconds in the runs I've been on, and certainly can't give any insight on yours, but that's where you need to be most watchful, and spend most your time trying to fix any mistakes. Mistakes later in the fight are usually fallout from mistakes earlier on, so there's less value in criticizing errors there.