while its doable to solo tank it / solo heal it, i dont recommend it. A lot of the garrosh encounter is proper preparation. Meaning: assign healing cooldowns to every whirling you will become later in the fight. assign players to each add in the first intermission , seperate the aoe stunners. If needed people can and should use offensive cds in that phase. I, as a combat rogue, make sure that i have killing spree and shadowblades/rush up when we get in the intermission. that way i can nearly solo 2 packs of the adds with my paladin tank stunning them (first pack kiling spree, second pack shadowblades). you should check for every aoe stun / silence before hand. Tauren war stomps and bloodelf silences are great in the first intermission. Use stampeding roar from a druid to move around faster.
for the add waves in the first intermission: you only need to stun them after the warsong is cast, have an eye on that. the stun rotation we use is: leg sweep (monk), mass grip (dk) on monk statue with binding shot (hunter), vortex (moonkin) and a shadowfury (warlock) if needed. At this point the iron star will roll in and the adds should be dealt with.
for the dps checks: we killed it after the nerf with 2 tanks and 2 healers, however had some p4 tries before the nerf went life. Meaning it's doable. For us, the tricky point was to survive the whirl dmg and kill the spawning adds without buffing them too much. You however can use your brewmaster tank to kite the adds from the whirl after the second intermission. i guess we had pretty good dps in our grp, as we got only 1 empowered whirl in p2 and 1 in p3 (with afking the second intermission that is) - i have seen a stream of a solo healing resto shaman which had rougly the same dps (~15% before going in second intermission). in the end it really depends on your group dps whether you have to drop a tank/healer or not
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2. aoe dmg is not the issue. the second pack has to be CCd, you wont kill them before the warsong hits, therefore its perfectly fine to send warlocks on engineer.
3. totally true. while you kill the last 2 packs in the intermission, make sure that everyside got a globe (the adds that spawn a globe are glowing), and wait like 2-3 seconds so that everyone can stand near a globe before triggering them. if one side doesnt have a globe. let the other side know, so that they wait with picking it up. Dont forget to attack garrosh though!
My 10man managed to get the first transition down with a very similar raid comp to yours (Prot Warrior/Prot Pally + Disc and Rdruid). The thing that made it repeatable was having our Rdruid take Heart of the Wild and go dps for the transition.
Make sure both tanks have some vengeance going in. Usually one holds him right when he finishes his floating deal in the middle, and about 2-3 seconds before transition, the other will taunt in.
If you're killing them in time but the boss is still gaining energy, then someone isn't hitting him with a physical attack to stop his energy. Heroic Throw seems to work while letting you stay out to get the buff with the group.