Yep, I know exactly what you are describing. I have had it happen before but never with the coil bent.
Maybe you could try removing the glass tank from the top instead of the bottom? You should be able to remove the drip tip and then unscrew the top metal part from the glass.
Let me see if this picture will post
Ok, this is a picture of the upper hardware without the glass tank. That top metal piece should unscrew from the glass tank.