You don't need a 3rd tank. And really in SoO the only fights off hand I can think of where a 3rd tank can be beneficial are Iron Jugg, Shamans, Nazgrim, and Garrosh. 7 healers is massive overkill. We ran 5 for normal and still only use 5 on heroic (we could still meet the enrage on heroic with 6 if we wanted).
You can probably do normal sending 2 dps at a time because you have at least some SoO gear now, but maybe not if you're taking 3 tanks and 7 healers. We did 3 dps per group on normal the first week though. We also only ever send 1 tank down. We use the healers and the dps who are about to go down to soak.
Too much Heals
Our comp is 3Tanks, 6 heals, and 16 DPS.
Going in 1st round - 1 tank, 5 DPS
2nd - 5 DPS (as soon as the 5 adds are dead)
3rd - 2nd tank and 3 DPS + 1 heal (again as soon as the adds are dead)
after that it is always 3 DPS and healers as soon the other is out.
We have about 30s before we hit berserk
oh Normal Norushen 2 Tanks, 6 heals and normally keep track that your healers gather the corruption and DPS stay clean. going in with 2 DPS at the time is manageable.