after watching the video's
my thoughts on this are that the acceration curve is too small
you can adjust this by widening that
also the threshhold can change this if it is widened
ramp rates can also change the speeds
throttle pot type if set wrong can cause this too
setting the max speeds M1, M2, M3 (if this is in fact a curtis controller) incorrectly can definatly cause the unit to jump to full speed if not set correctly.

One thing that most tech's don't realize is that every change you make on any one setting affects every setting in some way after that.
Best bet is to reset it back to factory defaults and start with changing the threshhold ranges and go from there.

i have dealt with a few of these curtis units (if that is what this is)
never seen a jungheinrich with a curtis controller in it before though, but that doesn't mean that the controller isn't made by them or after their design. And with all that being said it still does not mean there is not a problem with the tiller control, even though it may check good when you watch the throttle sweep on the handset, there still could be some other problem causing it to react this way.