Screw your die into your press from underneath with the die mouth facing up out the top of the press so you have a steady platform to work with. It's easier to see what's going on as you can get a lot of light into the die that way as well. EZ-Out or Tap should work.
I would just shove a bronze brush up into the brass and wiggle it tight..then pull it backout....the brushes should give you plenty of teeth to grab the brass solid
Who is the maker of the die? If it's case head separation good luck as it will need to be re-machined to removed the remaining brass and it's about the same price as a new die. Ask me how I know. Hopefully they will replace the die for you.
OR ….Send it back to the manufacturer.
It's safe to say it wouldn't be the first time that a stuck case body broke off in a die.
Beats being aggravated for 2 hours.
Just sayin'
Take a bolt that can fit into the case but will start to self Tap/ thread itself into the soft brass. Before hand, thread a nut onto the bolt thread with a washer large enough to sit on the die mouth. Once the bolt is threaded in well tighten down the nut and washer onto the die mouth. It's basically like a harmonic balancer or pulley extractor. Thread the die into the press before tightening the nut will help hold it. The nut and washer tightening will push against the die mouth pulling on the case and slowly pull it out.
To have it go even easier spray with penetration oil and put in the oven on warm for 15min . Alow the oil to get I there. Tighten the nut slowly. The bolt thread size could be so it cuts into the case body or small enough to cut into the neck but just not inbetween where it only cuts into the shoulder radius.
It's actually pretty easy in practice if you have a can orbox of extra bolts nuts of various sizes.
OR ….Send it back to the manufacturer.
It's safe to say it wouldn't be the first time that a stuck case body broke off in a die.
Beats being aggravated for 2 hours.
Just sayin'