I used a high speed drill, (air in my case, but a fast turning electric or Dremel should work too) and drilled a 1/16 hole through the broken pin as close to the center of it as possible. Once I felt the drill bit break through the old pin, I stopped the drill and waited about 10 seconds for the plastic that had melted from the heat of the drilling to solidify, and “weld” the pin to the drill bit. Then, without restarting the drill, or letting it turn on it's own, I just pulled straight out, being careful not to break the bit by letting it get on too much of an angle, and the pins came out along with the bit.
I just used a utility knife to “whittle” the remains of the old pin off the drill bit, and carried on to the next one.
It worked for me, hopefully it'll work for you too.
