#1) FIRST, while you cool off, let the gun/barrel cool off too. Coldest freezer you can find. Put it in for a while. Several hours. Over night. SOMETIMES, this will cause the metals to shrink enough --away from each other-- to let the case just fall out of the chamber. Or you might have to push on it with something gently or
Shot of WD 40 or other like spray before you cool it might help... or after... The super speed method is to run a liquid gas down the barrel and let it evaporate and cool. Propane. Butane. These you could pour onto the case section to cool it more/quicker...
#2). If this doesn't work, a healthy brass brush... a cleaning brush from the muzzle might catch enough brass to force it out. Or an oversize, shotgun brush or the like, into the brass to "grip" it.
OBVIOUSLY, the idea is to work the brass out without gouging the chamber and making huge problems. BE GENTLE and careful.
The final method, short of having a machinist "machine" it out, [EXPENSIVE], is to "cast" the chamber with a metal that will adhere to the case and bring it out when tapped out. Cerrosafe has done the deed many, many times. I guess there is a "babbit" that works. Pure or alloy lead could be used (with care). Sulphur would be awful flimsy. If you have unbelieveable finger skill, you might solder a wire or piece of metal to the sides to push on with a rod down the barrel. (I don't.)
The military makes and issues a "remover" that goes in ahead of the neck of the brass and expands when the threaded area is screwed in with a cleaning rod, but don't know of one of these in .35. Usually #1 or #2 get it quick... Brownells might.
As you indicate, you should be headspacing on the shoulder to lenghten brass life. Only the origina H&H's need the belt. Should be a long time before this happens again. Luck.