Anyobe tried cutting it down? Is it even possible?

 

Why would you cut it down? That's not what makes a short throw shifter. To make it a short throw shifter you simply raise the fulcrum. It can be done but no one has tried it. I haven't tried it because I like it just the way it is.

 

if you cut down the top part of the shifter it will simply reduce the travel of the shifter

 

The point of a short throw shifter is to reduce the throw angle. That also reduces the throw. If you shorten the shifter itself you still have the same throw angle and now have to reach further down to grab the shifter. Why not just do it right by raising the fulcrum? You don't have to cut the shifter and the grip point is the same but the shift throw and angle would be less.