Interestingly, SCH actually used to out perform WHM quite significantly in dungeons during HW.

1000 DPS was a realistic figure to aim for in Neverreap, the very first expert dungeon of the expansion and I distinctly remember doing more damage overall at the end of the expansion in dungeons like Baelsar's Wall.

Why? Because SCH generated most of it's AoE damage stacking dots and baneing them over the rest of the pull and dropping shadow flare ASAP. You had a GCD AoE to spam (Blizzard II) but it was a comparatively small portion of your damage vs WHM or AST which meant that when you did have to spend a GCD doing something other than nuking, you weren't penalised anything like as hard as the other healers. If you were having to heal through a rough pull with the tank not helping, most of your damage was still ticking away providing you were on the ball and getting things prepped as the pull was still in motion.

Of course SE did an SE and removed this, making SCH dependant on it's GCD nuke for aoe damage just like everyone else.

IMHO the solution is to move SCH back towards being more reliant for dot damage as it was in the past. That way it doesn't have the WHM raid contribution problem in reverse.