I will take a stab at it.
I would wire in a separate auxiliary battery
. It would be in parallel with your vehicle battery
, except, I would wire in a battery
solenoid that closes when your engine is running. This way, you have some power after you turn off the engine, without worrying about draining the battery. The inverter, (300 watts?) would then connect to the aux. battery. I would also think about getting a bigger inverter.
Be sure to size the wire to the aux battery, and to the inverter appropriately. The battery wire should be the same size as the wire from your current battery to the alternator. At 300W, your inverter should not be drawing much more then 25A.
I suppose you could skip the second battery, and just use the solenoid.