Just had a thought, @Susquatch can you make a new screw with a sleeve end (female) and fit it over the broken end of the screw? You might lose a little travel but you wouldn’t have to mess with getting the pivot end of the screw out of the leg.
You could join the sleeve to the old screw with one of the Loctite bushing retaining compounds. There certainly wouldn’t be much loading on the joint. You might be able to join the two halves of the existing screw with a bushing too. Maybe a nice shiny brass sleeve that shows that machinists can fix things elegantly.
The problem is that it's broken right at the middle of its travel. If I did this, I'd have to cut the remaining screw very short. Even the sleeve would have to be short and just at the very end. The new screw would have to be integral to the sleeve to yield enough thread. But it is a possibility. If I did that, I'd prolly just use steel epoxy.