There's one thing that makes this fight easier to heal.
Feral druid with PVP gear.
It does wonders for the unbalancing strike. Of course you still need to pound heals into the tank but it does away with the taunting back and forth tanks have to do. Just wait until the Feral dies and tank number 2 picks up the boss.
But I think you guys already run with the whole Feral druid and pvp gear.
Our normal set up is.
1 Holy priest, 2 Resto druid , 1 resto shaman and 2 paladins. We can do it with 5 healers. That's because our ranged DPS is too lazy to log on sometimes!
Prot paladin - Sits on the back taunting the add when mind control breaks. We use the priest in full frost resist to MC the add that gives the raid the rip off heroism buff.
Warrior- Sits around and picks up the boss around 7 -8 stacks ish. Thats when our Feral gets his face pounded in by.
Feral druid in PVP gear single tanking the boss for the most part.
It's possible to do it with 5 ish healers when first learning. Two tanks is a possibility if you aren't using the MC add and have a feral with PVP gear. We haven't missed the DPS check once with 6 healers and 3 tanks. I would be safe and suggest 5 healers and 2 tanks. 4 healers might be pushing it just a little bit imo with trying to down it first time.