Go with what I suggested earlier:
Top team: (8 players)
2 tanks, one tanks in center, one brings nagas, both trade off on vashj during stuns/roots
4 melee, on naga full time (they need to do 972+ dps each minimum to kill before next one spawns)
2 healers, one on tank, one CoH/chain/hot the tank and melee and optional shield disabler
Strider team: (5 players)
1 kiter, lock or elemental shaman works best, plus they can anhk so you get two chances
4 ranged, 730+ dps each minimum to only have one strider at a time (not counting kiter dps due to constant running and slowing)
Elemental teams (4): (12 players)
1 melee, ideally rogue or warior for sprint moves, at the waters edge
1 ranged, up top on that side, dps elementals, and strider as it goes by, and optional shield disabler
1 healer, up on the top edge, heals that sides melee, ranged, himself, and the off tank, kiter, and ranged dps as they run by
Keep the throw chain as [elemental melee] -> [elemental healer] -> [elemental ranged] to decouple core tossing as a self contained independent event on each side. Break up what seems like a complex fight into a bunch of smaller simple units and focus not on mastering the fight as a whole, but on mastering the units. When the simple units all start working, the fight as a whole automatically works. Try to always bring the same people in the same roles each attempt, so each group "bonds" and gets used to working together on their specific task.
Idea is to:
a) have the right amount of dps to minimize risk of elemental leaks and never have more than 1 naga or strider up. This is where you will have to know the dps numbers and meet the above requirements so you never have more than 1 naga/strider.
b) make each group responsible for everything in their area of operation so the load is evenly distributed, and make each group completely autonomous and self sufficient in killing their targets, healing themselves, and tossing cores.
Also when you get close to phase 3, wait until you get about 5 seconds before the next naga/strider spawn before you disable the last shield so your current adds are almost dead before you have to deal with vashj.
If you are really calculating, you can time the transition when the naga and strider timers coincide. If you don't miss a single core, that would be 200 seconds into phase 2, the next naga/strider overlap after obtaining the forth core would be 360 seconds. Thats actually enough time to miss 3 cores, and you'd end up killing 8 naga and 6 striders, and spend 6 minutes in phase 2, so that might be a bit much.