On our first kill, we had 2 weapons up (sword + shield) when phase 3 started, but back then we only had two mages and a warlock in the raid for AoE, so we didn't AoE at all. Since we started bringing 2-3 warlocks and 3-4 mages, we usually have 20-40 seconds before phase 3.
Again, on our first kill, we had two advisors up when phase 4 started (capernian and the engineer), nowadays we have none, or the engineer below 5%.
On our latest kill, with 5-6 new people, we had the shield up when phase 3 began, on about 5%, and the engineer when phase 4 started, around 8% HP.
As for healing, we usually have one healer on each of the advisor tanks (if they get focused by Thaladred, they notify the other healers who are on raid healing, and one of them takes over), so 4 of our 7 healers are usually free. By the time phase 4 starts, Thaladred and Sanguinar will be dead, which will grant the main tank 5 healers, which is plenty.
If you have trouble getting heals, tell your healers to be ready and at the appropriate place when phase 4 starts.