I love the formatting and the writing is a very easy fast paced read that has an excellent deliberate and straight forward style to it. I am always impressed and envious with how well you communicate your idea.
But I agree with all the others, the characters aren't really trapped in schemer's web as they are side stepping it. The PC have nothing to gain by getting involved and no motivation to do so other than clearing their name which as outsiders acused by a golden child of the city, would seem impossible, uncessary and at best a victory of principle only.
If they aren't interested in clearing their name then the PCs motivation will be to get as far away from the plot as possible. Perhaps a good courtly intrigue plot draws the characters into the plot rather than drives them away. As Vlad said, it is a railroad plot and the PCs should just run away. unless this is about clearing the PC's name. Yet the focus of this write up is not on clearing the PCs name, but shuffling them through a castle on a tour of The Five posts.
The intergration of the five does really just come as a gallery rather than a real weaving of the ideas into a story. The is best exemplified in the encounter with Blossom of Rage and the Kyth. As you have it written the smartest play would be for the PCs to sit and watch. Ara the blade just knocks them out leaves the story the and the write up does not give the PCs a path into Espeth's life or web. So there is a web and plot here but the story you have outlined seems to be the Free Parking-Advace to GO path around the board.
This is a really good space weapon, I love the detail. So I assume you envision the the plasma projectile moving slower than light.
I can already hear the players debating it merits.
Reasonable Player "It takes up too much space and has a low rate of fire"
Excitable Player "Yeah but only need to fire it once"
Meta-Player "The GM isn't going to let you take a bad guy with one shot, I don't care how big the gun is"