My stance is basically this: The healers should, for the most part, mirror the tanks in regards to how they approach offense with slightly fewer, yet more readily available options for healing tools (i.e. some combination of shorter cooldowns, charges, and shared resources like the lilies).

WHM: Reflects a midpoint between Warrior and Paladin complexity. Methodical, but designed to be very forgiving.
SCH: Reflects Dark Knight complexity. Make Aetherflow all about damage and somewhat bursty while Fey Gauge is all about healing, but with a way to convert Aetherflow to Fey Gauge in emergencies.
SGE: Reflects Gunbreaker complexity. Feels like a mini DPS. Shift gears away from Addersgall as your main source of healing and toward Kardia instead.

AST: Does not reflect any tank. AST is a support engine builder who spends their GCD setting up engines for healing, for offensive buffs, and for utility to detonate as needed while generating DPS for other players to execute with a reworked Synastry similar to Dance Partner or Kardia. Can still do this themselves while soloing, and perhaps their buffs become attacks when you apply that Synastry to yourself for the purposes of soloing. Weaker than supporting your team, but useful for solo duties and deep dungeons.