So the barrel is definitely clogged, and not the nozzle? Did the nozzle come off? If you have the nozzle and the heatcore off so it is just the brass barrel sticking out of the black PEEK, is the plastic inside the barrel the color it is supposed to be, or is it brown or blackened?
Does it look like this-

Or this -

If it is like the top picture, I wouldn't recommend trying to get it out. If it is like the bottom, then you should try to remove it. If the nozzle is completely clean and it still won't extrude, then there might be a problem at the junction between the PEEK and the top of the barrel inside.
The only reason I removed the barrel from the PEEK was it was loose enough that when I tried to unscrew the nozzle the barrel would unscrew from the PEEK instead. If the plastic inside the barrel is burned, then you can try heating the end of it with the torch and trying to unscrew it every few seconds as the heat travels up the barrel to the plastic. Don't try to twist the barrel too hard, because it will break more easily than you would expect.