How do I use Lithium Polymer batteries in a very high draw system without tripping the overload protection?
If you continue to use a 12V battery, you could limit the current by using a heating element with more resistance, or by placing multiple heating elements in series. If you place 2 of your elements in series, that should cut the current in half.

Another way to lower the current would be to use a battery with a lower voltage. You can buy 3.7V lithium batteries online (one option). The 12V lithium batteries are probably 4 lithium cells in series, so using one of these 3.7V batteries should cut the current running through your circuit by 75%.

If you use a lower voltage battery, you may still need to raise the resistance of the heating element by using a different element, or putting multiple in series, in order to stay within the current rating of the battery.