i have had the same problem, with the pin breaking. and yes i tried pressing it that was a no no . when my pin broke in the tool it also jammed in it.
here is a solution
when pin breaks in tool if it doesnt some out drill a 1.2mm hole in the other end of it right down the full lenght then you can insert a metal rod of 1mm and push wots left out .next take your 3mmby 17 mm drive pin put it in the dremmel and put heavy sanding paper on it ,turn it down to 2.7mm both ends ,it doesnt have to be exact then buff a flat on one end for the set screw 1 new pin made what i found it needed was that the shaft required heat round the old pin then put it in the extractor slide the other bit in and hit with very large hammer one or twice falls straight out no hasstle im using a 1.5kg hammer
if your real unlucky and pin breaks again make a new one .they are so hard thats why the break
i know its not ideal but it works the first 2 shafts i did i broke pins the next 10 came out no problems hope this helps its a great tool just go with the flow