My ideas are fairly simple and straight-forward, but I hope someone on the design team might take some inspiration for this, as the current community-enforced methods for leveling in Eureka tend to be heavily against people even two days late to the content.
The first is simply scaling the frequency of FATEs based on their difficulty, where the upper end (say the top 5 levels per area) take roughly the same lockout period of two hours, but instead reduce the amount of time it takes for ones of a lower difficulty to become available again, maybe at a minimum of once per 30 minutes for the lowest level FATE for an area in Eureka. Compounding upon this, lowering the relative levels of the mobs needed to spawn early FATEs would help as well, say to a level discrepancy of three or less in between at the lower level mobs needed to spawn it and the FATE itself, as the current discrepancy of five levels between what is needed to spawn a FATE boss and the boss itself is fairly high (level 6 to spawn a level 1 FATE, totally fair to newbs right?).
There could also be more FATE bosses available at the lower levels from different mobs, such that there is more to do/find at those levels. That said, I think the most effective thing to do would be to apply a new system within Eureka that is from current and old content: Daily/Weekly side quests that scale to your (in Eureka) level that can be completed solo which provide their own currency or separate rewards. There is no reason this cannot be implemented in Eureka as there are already in-instance-level related quests and the code for scaling like this is used already for both the Heavensward and Stormblood Beast tribes. At the upper end, this could also serve to be a source of extra items, potentially have it such that once maxed (for the area) you get a token from these daily/weekly quests that can be traded up for part of an upgrade material (say x amount for a single Pazuzu feather in current content) or a specific reward that could draw in people that may otherwise not enter (such as crafting/gathering Grade 6s, since there isn't a direct way to get them outside of getting lucky with transmutation or getting lucky on WT).
These are just a few ideas I had brainstormed a while back and never got the chance to post due to life related issues, I'd love to see some constructive feedback on them if possible.