Me personally have no problem healing my WAR tank in The Coil of Bahamut Turn 1 as a SCH.
And that is with having Eos in the middle of the party to raidheal, while our WHM heals our PLD, maybe throwing out a Medica II if its getting a little tight.

Also had no problem doing the Main Tank healing on Titan Hard, with my Warrior Tank.

Haven't tried Turn 2 yet.