Quite the interesting premise this series has! Now added to my Audible wishlist, FYI.
After further pondering, here are my current tentative predictions on which factions are most likely to become the G5 Big Three:
1- Hegemony Remnant: Led by Kleitos’ heir, Phaedrx, the Remnant has barely survived the Siege of Aekos, and now seeks to rally its remaining loyalists (and potentially unexpected new allies) to restoring Kleitos’ dynasty/reign as Thaumatarchs.
2- The Cult of Vigil: Perhaps Vigil is not just some inanimate Theurgic battery with vaguely defined “negative vibes”; maybe it’s some sort of sentient, crash-landed alien who was responsible for teaching humanity the secrets of Theurgy? (and was then eventually sealed away by Hera after losing an epic duel against her) Perhaps Vigil has been biding his time, licking his wounds, and (privately) gathering his own flock of worshippers across the Hegemony’s centuries of existence? (and will interpret the Xaos-storming of Grand Shayard’s City Ward as the perfect moment to come out of hiding)
As for Vigil’s hypothetical goals: get revenge on Hera by seizing control of the Hegemony’s territories (and by undertaking some elaborate scheme to monopolize control of Theurgy/blood/Aether for itself).
3- New Brauracha: Tripartite alliance between (secretly surviving) Braurachan Theurges, Halassur, and Nyrish “fifth columnists.” If MC ends up antagonizing/alienating all of Nyryal, then the alliance expands to include most/all of Nyryal accordingly.
@Havenstone (Overlapping with past questions about the Hanseatic League and Carthaginian Empire analogies)
For imperialist MCs whose most powerful supporters are the merchant and pirating communities, will it be a viable/sustainable strategy to to deliberately limit their faction’s G5 scope of conquest to (nearly) everybody else’s major trade ports? (Aka the Portuguese imperial approach, which led to Portugal becoming “the spice daddy of Europe”)
And on another note, I aim to avoid repeating Portugal’s mistake of antagonizing/exiling my religious minority allies into becoming my worst economic enemies. (E.g. exiled Portuguese Jews banded together/resettled in Holland to form the Dutch East India Company/VoC).
I like the way you think! 
But I’d like to take that prediction one step further: what if Breden is the “Gryphon claimant with much, much deeper historical roots?”
Your thoughts on the iconic “keep your friends close, and enemies closer” quote? (and why it’s not worth keeping Breden close for the duplicitous purpose of eventually exposing and/or offing them)