In that situation, IMO WHM actually has the best chances of dealing with such a pull. Why? Holy. I don't know if the WHM used it, but it is what makes WHM the best (easiest) dungeon healer by far.

For the other healers, I think SCH and AST could probably survive that situation as well, but with more effort needed (and I'm not sure if SCH would make it mana-wise). SGE would have (IMO) no chance in hell with the limited spells they have at that level (Kardia, Soteria, (E) Diagnosis, Physis, Druochole).

WHM has issues, definitely. But there's no need to downplay it's strengths either.