How about update the Hunting Log to a "full" bestiary log (with photos) for the entire game, including Fate/Dungeon/Trials/Raids, etc.

Advanced mode (Tier II)could include positions on maps just like gathering log.

Advanced+ Mode(Tier III) mode could give daily or weekly % modifiers for monsters to drop crafting loot.

Advanced++ Mode (Tier IV) could be a weekly target for each type of content to unlock +25-50 crafting items ?

You could go up in tiers until you've unlock all Bestiary tiers by completed X amount of completions?