Why is chilipeppr adding a z-axis offset by itself?

From what I can see your Gcode file has a G54 at the start of it. That could be causing your jump. Could you possibly try just running the ChiliPeppr logo Gcode after you do the Touch Plate? That logo Gcode has no work coordinate system overrides going on, so I’m wondering then if you run it after the Touch Plate if you don’t see the jump.