I am a SCH main and I have leveled and used all three healers so far in 80 Extremes and Savage.

I think WHM is currently the best designed of all three.
I don't think WHM needs a Lilly dump, rather I'd give it the ability to weave lilly healing between casts by making Afflatus Rapture and Solace into oGCDs.

If anything I'd make Fluid Aura increase the speed of lilly production either increasing the lilly gauge by one or speeding up the generation by X for X seconds.

All changes would require to adjust potencies of course.

WHM feels a bit clunky. I wish you'd be able to weave spells better.