This puzzle is not yet solved. Potential spoilers in the section below.
Discussion section for The Bully Pulpit
The story text indicates cutting off the heads of all those who try to escape. Based on that I spent a (very) small amount of time identify the authors from the library card at the front of the book. Unfortunately, I don't have the physical card, it's not in the PDF, and the printout has some very blurry names.
Anyway, a few short minutes didn't turn anything up, but the idea seemed vaguely sound.
Other than that, I'd have to imagine that Scraps of Vellum #2 will give a set of instructions for the final puzzle.
Some people on other forums said to look in the artwork on each page for clues. I find that unlikely, on this theory: Samuel and Colleen solved the puzzle. They didn't have the artwork; they only had the deck of cards, and the puzzles, and the 52 scraps of paper just picked up, and the Minotaur's instructions. So it must be solvable with that.
^ This last part isn't strictly true; the Gatekeeper gave Colleen and Samuel the library copy of The Maze of Games in "The Olympic Spirit", and Colleen explicitly remarks on the illustrations. I think it very likely the illustrations contain puzzle-vital information. So the siblings have: a deck of cards with joker; the scraps of vellum; the entire book of the Maze of Games, minus the pages at the end (I assume from the start of chapter 5 onward); and the mace and dagger they got earlier. The solution must be obtained with only those things.
Let us assume that Theseus, who previously beat the Maze, had a clue, or a "ball of string" as described in the text (3rd paragraph from the end) in the section entitled For Want of a Clue. Now let's further assume that these are the letters that get plugged into The Hidden Goal (lowercase where a lower box and uppercase where an upper box), we get:
Mapping these to the scraps of parchment, we would get:
You'll walk so far before you're done,
Should you live to see the sun.
Low-lit tunnels do conceal
A way that you might rightly feel.
When you fear you'll tread no more,
So many chambers you'll explore.
You fight the forces immaterial,
Dangerous but yet ethereal.
Terror always follows close,
Leaving victims quite morose.
Your journey on this path's accounted
By your losses, ever mounted.
Men of power, wealth, and station
Loathe your dire situation.
Look alive! No need to brood!
Here your fate has been reviewed.
If bedevilments appear,
You'd say there's something fishy here.
Despite your honest preparations,
You will face its dark temptations.
Peruse your tome and you may see
The way to reach your destiny.
Now you travel near and far
Protected like the bairns you are.
I believe this is the starting point. Now I think we need to find the answers that fit that involve beheading. Either of the answers themselves or of the objects the kids found in the maze, but "lost".
One approach: in the Ace of Diamonds puzzle, Samuel loses the tip of his SWORD -- S+WORD maybe? In Four of Diamonds puzzle, Colleen lost a HAIR that was split: H+AIR. In Eight of Diamonds, Colleen loses a HAT -- H+AT maybe?Maybe something here?