I think if you give WHM the DPS of a DPS, you risk replacing DPS. The SCH approach might work: increase WHM healing potential while in full DPS rotation.

Imagine if Regen got a potency buff, could generate lilies on HP restoral / reduce cds / give confession (similar to cure in SB), and could be used off gcd similar to the way energy drain's CD works. Then, buff lily CD reduction to be a bit more meaningful​

WHM would be a monster, having a substantial aptitude for delivering healing without halting it's DPS. I could see a WHM/NAST combo working very well, where WHM DPSes and helps fill the NASTs hps. SCH / WHM could be a decent option as well, as both classes could push substantial DPS and healing/mitigation at the same time w/o worrying about balance rng.