A little addition if you try to remove broken screws by yourself.First thing you need to do is get rid of the old cork seal,either heat or pick it out.The seal is the creator of the problem,over the years it turns rock hard and makes removing almost impossible without breaking.If I get three sixpack set to do I can guarantee at least two broken screws minimum.Also if you choose to drill,a small end mill is almost a necessity,unless you have a perfectly flat surface to drill,the drill bit will walk and not center.Once I get them drilled,I use a small center punch with the end squared,tap it into the hole and back the screw out,picture attached.