Go Grab-tastic on every piece of gear from every dungeon you run, need / greed the lot of it. Trade it in for GC seals and use them to obtain cordials, coke, animal fat, etc, whatever sells well on the market.
Hard Mode primals may potentially be a benefit for items from Ifrit, Garuda, Titan and Leviathan since they are needed to craft the minions.
Rank 3 ARR beast tribe quests give 1 T4 materia each. (Kobold, Sahagin, Sylph and Amal'jaa)