Call me a heaven if you may, but what about weaving by using Regen or clipping the A2 dot a bit earlier in favour of weaving? I know that isn't the most dps-friendly solution, but I don't know what else to say that may sound like a solution.

Understandably the meta for healing is minimizing healing gcds and maximizing dps potency, but don't you think WHM is more than well equipped with the best mana economy, more healing ogcds and the most accessible burst heal, only limited by MP? There gotta be some trade-off for all the goodies and that is efficient weaving potential.