You can't "continue" the existing quest with WHM instead of DRG.
You can restart that stage of the anima with WHM if you finish it with DRG. You can also wait until you have all of the crystals (or more), then abandon the DRG version and pick up the WHM version - you don't lose the crystals if you abandon the quest.

In general - if something (even a quest item) is in your inventory you won't lose it if you abandon the quest. If it is in Key Items then you might.