Written by Tara Holm and Justin Legakis
The given text is the result of interleaving, sentence by sentence, three different riddle trails. Each of these trails spends much of its length in a single geometrical plane P, consisting of the Infinite Corridor, the corresponding corridors above and below it, and the elevators and stairways connecting them, as shown here:
The three trails all converge at the end in Killian Court. Some portions of the trails overlap (as hinted at by "We couldn't believe we hadn't run into each other"). When the plane P is viewed from the Killian Court side ("Pondering where we had been, we stopped to admire the view"), these overlapping segments, shown here:
spell out the solution, JELL.