right the way i see it is that with a short shifter, the shaft beneath the pivot point is longer then there is more leverage therefore the gear will be selected soon with less movement of the gear stick above the pivot point correct?
if you simply chop the shaft down then the actual throw is not reduced, the angle of the gear stick remains the same, it may look like a shorter throw but that is just becasuse the shaft is shorter therefore the gearknob will not seem as far forward or backwards as before it was chopped. Also if you simpy cut the shaft down you will need more effort to change gear because of the reduced leverage.
if you simply chop the shaft down then the actual throw is not reduced, the angle of the gear stick remains the same, it may look like a shorter throw but that is just becasuse the shaft is shorter therefore the gearknob will not seem as far forward or backwards as before it was chopped. Also if you simpy cut the shaft down you will need more effort to change gear because of the reduced leverage.