Yip, they can be a pain if the end of the wire has snapped. Unfortunately it's just a case of pursevering and getting something in behind the wire to flick it out as you turn the top head. I think I'd be inclined to pull the cylinder and lay it sideways in the vice so you can get a good steady continuous turn on the cap as opposed to small turns with cylinder insitu.

unfortunately it can be that complicated
it should unscrew in normal direction. like a jam jar
but if the ends of the wire are broken off, can be a real pain
best get a crown tech who has dealt with this before
can take hours if both ends are broken off