Just wanted to let you know how helpful your detailed post was.
I would not have attempted this repair without your instructions. I'm sitting at the kitchen table with a fully repaired unit in front of me. My problem was the same shaft that you showed broken off was also broken off.
To repair it, I took a nail that was very close to the same dia. and spun it in a drill against a file and finished it with the sanding tape plumbers use. Took about 6 1000's off to match the broken shaft. Drilled a perfectly centered hole thru the case and then measured the nail against the plastic shaft and cut it to length with a dremel. Final step was to put epoxy under the nail head outside the case without getting any inside on the polished shaft. I put the case halves together without gears overnight to be sure the shaft stood straight and cleanly engaged in the hole in the opposite case half. Perfect!
A little trick to avoid breaking off the case clips as some others reported was to gently pry them back with flat toothpicks and leaving all 6 picks in place while carefully prying the halves apart with a thin screwdriver being careful to work evenly around around the case and pulling the halves straight apart.
The dealer from whom we bought our Salsa '05 quoted me $90 for a new actuator and $88 for installation...I spent $30 and bought a set of extensions, a universal and metric sockets for my 1/8" socket set
Final point, I pried the center dash bezel off and reached thru there to loosen the top screw as another member posted.
It all worked great thanks to this wonderful forum!!! If this arthritic 67 year old can do it, anyone can.