I had this problem with a few Mercury models some time ago.

I couldn't get the 'stumps' out and sold the models on.

I think the best way of replacing a broken mast is to drill a hole, very carefully, immediately adjacent to the mast. This must be on the centre line of course.

Drill the dole as deep as you can - there might be a risk of drilling through the casting, but this might actually help in the end. Once you have your hole replace the mast with a brass rod and epoxy it in place. This could be underneath too if you have drilled through.

Alternatively, if you can, live with no masts.