Back in the '90s, I was able to get one out by using a short piece of lawnmower throttle cable wire to drive out the old wire. I can't remember how I held it, probably with vice grips as close to the hole as possible. And probably going the other direction, not against the end that broke. It also seems like I sawed the access slot a bit longer at some point during that episode. Do the penetrating oil soak, the bump the shaft back and forth, etc. first.
I also used the lawnmower cable wire for the new clip.