My Eureka Concept

[Nezerius]

Flying is disabled at first, but can be activated for a brief time under certain conditions.

[...]Travel Feathers (key item that allows flying in Eureka for 5 minutes for the whole party, disappears when duty ends)[...]

This just sound like a terribly frustrating idea, especially given your example of the area's size (Azys Lla is a pretty big zone). There'd be nothing fun about getting a boss spawning on the other side of the map.
You'll either have to just have a set objective that enables for the entirety of the instance timer, or decrease the size of the map.

Cost to Enter:
In DF it charges 200 per player upon zoning in. In PF any # of players can contribute any amount of tomes to reach the total 800.

Why is it that a DF group gets a total cost of 1600 tomes? That seems like a silly "incentive" to get people to use the PF. Just leave it at 100 tomes per person, the same as the total cost of a PF group.

Difficulty:
The key items needed to boost the star rating aren't super rare, but they aren't common either.

What's the point of setting the difficulty, when you have to rely on RNG to even start it at the difficulty that you want your group to tackle it at? Just give players the freedom to set the difficulty.
If you really want to have some way of "unlocking" higher difficulties, perhaps some type of attunement would be better. Like clearing the last savage turn of the current raid to permanently unlock the highest difficulty.

Time Limit:
The default time limit is 30 minutes. You can extend this in PF groups only by supplying a key item "Hourglass of Time". This item can be obtained via crafters. Each one increases the duration by 10 minutes.

I can already see the PF comments. "LF x MORE FOR EUREKA - MUST HAVE 1 HOURGLASS OF TIME TO JOIN"

At which point, you might as well just set it to a normal instance timer.

The monster stuff seems okay, though it might be tricky to pull bosses from other types of content, while retaining the possibility of each having 15+ mechanics.