During our 25man kills we've had everyone spread out in Phase 1. A few healers assigned to tank, and spreading out the healers on the raid, much like Penetrating Cold on Anub'Arak in Trial of the Crusader, as to not waste mana. If you can be pretty sure that no two raid healers are healing the same target, you can use faster heals without wasting too much mana. As for the massacre, utilize priests prayers and group heals, you don't need to keep anyone above 10k so it should be fairly easy.
In Phase 2, when the bot is recovering, stack everyone in the middle and try to rotate healing cooldowns in this phase. Once it's over, you should wait for the first massacre, since everyone is grouped already, heal that, then spread out again. The time between the first massacre after feud and the next spit thing is enough for everyone to spread out again.
Then just keep doing that until it feels alright, healers will learn to conserve mana where possible. Just make sure the tanks are topped before Phase 3, and have everyone use their last mana on nuking the boss.