As there have been no substantial nerfs to the Eureka weapon progression outside of the NM tweaks and slight gains to vitiated aether in certain zones. I would offer some improvements to provide incentive to complete subsequent Eureka weapons.

First, the challenge log awards elemental exp and gil for completing those entries. Max-level players do not necessarily get anything from this outside of the occasional need to re-level. I would ask that an adjustment be made to replace the elemetal exp for players at max-level with a portion of Amenos, Pagos, Pyros, and Hydatos crystals. And vitiated aether yields for both Pagos and Pyros.

Next, I would ask for daily ojectives/quests added to each zone in Eureka. I am sure someone employed at each camp could use help with a mundane task: retrieving this or that, killing a handful of certain mobs, etc. These quests would reward players with that zone's resources for the Eureka weapon.

If adjustments to the challenge log are not feasible, due to the reward structure of the log, I would offer an alternative. Add a weekly quest to award the crystals/vitiated aether yields instead. Potentially something along the lines of exchanging one of each Pazuzu feather, Louhi tear, Penthesilea flame, and Crystalline scale for the quest completion.