Dafydd,
If you intend to go with a linear voltage regulator, please get some advice on cooling. The heatsink required to cool your 18watts (in still air) is quite large. Whilst the linear regulator is a great way to smooth the pulses out (as long as pre-filtering prevents any spikes exceeding the regulator's max input spec), you will find that the same pulse suppression can be achieved with a normal good quality switched mode design. Also, the switch mode unit is available 'off the shelf' with all that suppression built in. Well, at least that is true if you buy a quality unit.
I have not yet seen data on the Jabiru or Rotax regulators.
However, the Rotax 912 coils that I replaced were a three phase type branded Ducati.
"Normal" motorcycle regulators ( and I expect that Ducati would design their coils to suit this) rely on a 'short circuit' type regulator. I have tested these on motorcycles. NOT in ROTAX. These work by triggering a SCR to short each coil when the terminal voltage reaches 14 volts. It does this each cycle of the output voltage. So you get pulses of 14 volts going to the battery and the battery 'holds over' until the next pulse of 14 volts. Any excess power is dissipated in the coils themselves. I have put a oscilloscope across it and there are spikes of about 20 volts superimposed on the switching instants. You will find that any good automotive plugin device should not be bothered by this. I am aware that other small engines use single phase of the same concept, and similar regulators. Note that this is not a true switch mode regulator. Maybe it could be called a shunt regulator. If a true switch (series) mode regulator was employed, the potential generator coil voltage could spike much higher when the regulator pulses off. I would expect that the coils would have to be designed with better insulation to withstand this. Also there would have to be a spike suppression of some sort, but that is just an assumption.
Pete
PS don't use cigarette lighter sockets