A dungeon-like event where you can make Gil? Erm . . Treasure Maps? I make a ton of Gil from doing current group ones with members of our FC. Even before selling dropped mats (which some go for a lot of money and are sought after crafting materials so sell reasonably quickly) you can walk away with a few hundred thousand gil after a short session.

The whole idea around relics is to make them a slog to get - if they/the mats dropped so easily, they wouldn't be special. That said, older relics aren't that hard to get - I got my ARR White Mage staff (I wanted the title) within 45 minutes of starting it.

As Stepjam already said, everything but Ultimates, Eureka and Bozja can be unsynced already.