Shorting the probes like that should have given a resistance close to zero, certainly under one ohm. It seems like you are getting lots of bad connections. Try cleaning your probes with high purity alcohol (isopropanol, ethanol or methanol doesn't matter which) on a wadded up paper towel, twisting the probe while pinching it firmly in a fold of the paper towel. For the rivets on the heating element and the battery contacts, try wiping them with alcohol, and if that doesn't decrease the contact resistance significantly and make it more stable, lightly abrade them with either a fibreglass pencil brush (preferred), 800 grit or finer wet&dry paper, or a typist's erasor (abrasive rubber), then re-clean with alcohol.