I don't follow Parelli too closely, aside from a working knowledge of the philosophy and techniques, but I'm kinda with Flitterbug on this one. I wouldn't lose the stick, at least not forever. Maybe work without it for a while (use a coil of rope for impulsion and fingertips for things like the Porcupine Game), and establish some trust and respect there, and reintroduce the stick at a later date, and in the way that Flitterbug has suggested. Just tote it around with you. Shoot, if it's an extension of your arm, let him think that it's really attached!
I'd go so far as to leave the stick in his paddock while he's turned out, or in sight of his stall while he's in, as long as
the fear isn't so bad that the presence of the stick itself puts him into a full-on flight response that doesn't abate until the stick is taken away.
Another thing that may help, and is a little more structured, is to put a halter and lead on him, carry the stick, and walk away, letting him "chase" the scary object. As he gets comfortable, up the stakes, and judiciously push his thresholds. March, waving the thing like a drum major, while he follows. Spin the string like a helicopter over your head, while he follows.
I am concerned about the timetable, as well. Horses have no concept of timetables, and if you push one to make a show or event you run a very real risk of leaving gaps in training, and rushing. Setting goals is fine, planning to go to a show is fine, but when they have a date attached by which the horse must know all, things can go south. I do believe I quote Mr. Parelli - "Take the time it takes so it takes less time."