Hrm, 12 shards is a lot of shards (that's like, 1,200 gil alone on my server), but you're right that the other mats are trivial. I'll add it to the above.

Someone (meaning, probably me unless there are other crazy obsessive people out there) should desynth ~100 items each of different ilvls and see if the ilvl affects the chance to get Demimateria or not. I'd have done it by now, but I'm too busy fishing and hoping that some tradable Big Fish yields Waterproof Cotton so I don't have to drop a desynth class for CUL.

OP updated with an ARM guide and a CRP guide (thanks to Lyrinn for the CRP advice!)