It will change based on DIRECTION not POSITION. Light in the sky comes from one source, the sun. It scatters through the air molecules, dust, water vapor,etc. Due to the scattering, a polarizer is more effective in one direction than another. It does not mean its ineffective, it just means its more effective.
If your camera angle changes relative to the sun during the zipline move, yes the effect of the polarizer will change. Since you can't go up and twist it by hand, your only choice is to choose the mid point. At the two ends of the angle arc, the polarizer won't be as effective but by choosing the middle (or the angle where most of the video will be shot), you at least cover the majority of the needed angles.
Wish I had some polarizer gel I could whip up a filter from so I could show you.