Ohm's Law is at play here. Ohm's Law states: resistance of the circuit is equal to the voltage divided by amperage, or R=V/A. The LED is lower wattage than a Halogen by about 1/3. Reducing the wattage in the circuit is the same as lowering the resistance. In your GL1000, the current (watts or volt times amperage) is constant. Lower the resistance, current is constant then the voltage must go up to keep the formula balanced... or so Ohm says. The only reason to have the LED is if you like it. If you want to keep it I would suggest a modern voltage regulator such as Rick's MOS FET regulator. Above 14 volts will cause the battery to boil off faster. You will need to keep a closer eye on the battery electrolyte level until this gets sorted out.
Thanks! Do you think as long as I don't let the battery run dry it should be ok? Also do you know if that Ricks MOSFET regulator is an exact replacement without having to do any wiring?