We see this a LOT here in the shop, and can remove the broken off screws as we're pretty good at it.
They are difficult to drill out and stay on center as you found out, it takes special procedures and very good drill bits to be successful at that deal.
Removing the linkage from the end of the shaft requires that you grind off the staked portion then drive or press out the shaft, then install a different one. No new ones available that I know of, so it will need to come from another used one, 1975 or newer style carb (longer than the older style).
Good news is that we may have a few of those throttle shafts in the shop with the linkage already on them. Hopefully you got one of our kits for the rebuild as well. Our kits contain parts far superior to what others are offering, and our accelerator pump seal has a lifetime warranty on it.....Cliff