Since monster learning is out of the question in FFXIV, I find that another option could be from the garleans themselves. Since they already into allagan tech and willing to gather more knowledge from the civilization that combat and contain the primals and others for global conquest and more. Why not use that knowledge into a smaller scale towards the player. A blunt weapon made to syphon part of the aether of the primals and use it to combat them. Like w/ SMNs that requires basically a pact to use a part of them to combat against the primals, BLU steals a part of them to combat the primals. While at the same time w/ allagan tech from ultima, omega, etc., that type of knowledge can be used as a way to enhance BLUs abilities to combat against the primals as in weakening their magic attack, defense, buff party, etc.

This idea just came on a whim to try to be a part of FFXIV lore or to fit into it. Why I add blunt into this? Cause there's only 1 job that uses blunt literally.......