I'd try to get a flathead screwdriver a size so it just barely catches that outer part of the brass and slides inside the brass bit. Then gently drive it down so it bottoms out inside there.
It shouldn't be that tight so it just needs a bit of help. Just be careful because if you put it in there like a wedge it'll make it tighter.
^^ This won't make any dust or pieces and if it doesn't work no harm done.
Another thing you could do is get a drop of JB weld on a very small bolt or something and stick it to the bottom of the brass part upright. Let it cure and try to back the bolt out hopefully taking the brass bit with it.
^^ These are both assuming the lowest brass bottom is part of what broke off.
Or an easy-out (but gotta be on your A game with that.
It shouldn't be that tight so it just needs a bit of help. Just be careful because if you put it in there like a wedge it'll make it tighter.
^^ This won't make any dust or pieces and if it doesn't work no harm done.
Another thing you could do is get a drop of JB weld on a very small bolt or something and stick it to the bottom of the brass part upright. Let it cure and try to back the bolt out hopefully taking the brass bit with it.
^^ These are both assuming the lowest brass bottom is part of what broke off.
Or an easy-out (but gotta be on your A game with that.
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