Ive never had a bucket stuck in a head but there are many things you can do. Weld a bolt tot the top and yank it out with a slidehammer. Cut the center out of the valve with a dremel and tap the valve stem out from the bottom. Just how stuck is it? A good magnet usually can pull one out. You can also drill a hole and intall a screw into the top of the bucket . Just dont do anything crazy or you get to buy a new head. Or you can send it to me and Ill show it who is boss.
It's STUCK, no magnet is gettin it out. I'll try the drill and screw method, thanks bud. I might end up sendin it to you and letting you go to town on it haha
Make sure you drill it off-center to not hit the shim... like 2 holes for 2 screws to twist and pull it out evenly. If the mated valve is not dropped, the bucket is still high and some limited downward rap to the bucket-center might loosen it up first. Fun fun, hope you can save the boreway