Yep, unbalancing the party with giving boons to some and none to others can cause trouble even within good friends' partys. And also yep, the Rites, and, depending on the focus of your party, the title and narrative power that comes along with being Monarch can shake things up if you are not careful.
So what can you do?
First, make sure to not funnel all the cool stuff to only a few players or, worse, only one. Unless there are characters that really don't care for the narrative (just give them numerical boni then). Be thoughtful with items like the Urn, the Huble Hook, the Blades of Srasama or the Arsenal of Dhabisu. And, if it feels appropriate, expand upon them.
Second, make sure that every character has a niche/specific role to play once you reach "epic tier".
Third, what
@RangerWickett said... this world is full of mystery, old and new rituals and technology. Do not limit yourself by strictly adhering to the game's rules because the adventure surely doesn't. Let the monarch share their powers or create new positions. Use fey stuff. Added bloodlines.
For myself, I was quite happy that my other player (the one whose PC became monarch) thought about a fitting new position for my PC and a corresponding set of powers. Because the in-character power imbalance between someone at the top of the nation and someone still working for Delft was... unsettling.
Also... could you theoretically exploit the Green Knights' powers in a post-gyre world as technically the sun won't be out anymore? Or would the vanishing of Av shatter her power source? (always wanted to ask that question
)