Battlecraft III became insanely devalued when it became able to drop from white crafted Stormblood items. I have no idea why they did that. It wasn't particularly hard to get to begin with, considering all the stuff it drops from.

Fieldcraft III and Mastercraft Demimateria are quite valuable. You may also be able to get good mileage out of desynthing items that can drop Glass Fibers. I just wish they'd add another desynth-unique item.