Mike - the least intrusive thing you can try is to use a magnet to try to manipulate the coil with. Let the lamp heat up and then try to see if you can pull the coil up from the bottom of the bottle and then manipulate with a magnet or two.
Hmmm the metal seems too thin, Im using a high powered magnet too. One from a hard disk. How did this even happen I have 3 lava lamps and I turned this one on and was like whaaaaa