@ Aspenkarius:
FORGET you ever heard about Easy-outs or threading Taps or anything else. You do NOT want a completely-scrood chamber in your rifle.
Try what we did in the Army: run another round up the pipe, let it latch onto the on stuck in the Chamber, then give the Bolt good, smart yank to the rear. Chances are 98 out of 100 that it will bring them BOTH out.
If that fails, THEN get onto the EE and find yourself a proper Stuck Case Remover. It is the PROPER tool for the job and it WORKS. Worth maybe 15 bucks.
As an interim measure, I have found that you can run a cleaning rod THROUGH the broken casing and out the Muzzle, attach a TIGHT patch and pull the rod out of the rear of the rifle. Generally it will bring the offending cartridge with it.
If your cases are breaking off IN the rifle, chances are 9 out of 10 that they are TOO LONG. Keep your brass trimmed to 2.20". MUCH .303 brass lengthens far MORE in the reloading die than it does in the Rifle. The Americans don't understand the .303. Besides, almost any American knows that the .303 is junk.
Using an O-ring on the FIRST firing and then neck-sizing only can give you 20 shots per casing and still looking good.
Try it.
Works for me.