My problem is, the center section of the rivets--the piece that the rivet gun grabs hold of, and which breaks off once it's riveted--is too short to grab with my gun.

First off, the gun can't get down against the head because the rivet is so close the the tall threaded section of the guide. So, I used a small washer--about 1/2" long--to slide over the center section, which basically works to extend the head of my rivet gun. However, doing this causes the center section to be too short for the gun to grab onto, like I mentioned above.

Here's the STI guide: http://www.cycle-frames.com/bicycle-...-STI-STOP.html

It's the same basic guide everyone else uses, so how do you guys rivet it in place?