use a choke?
i would have to do some tests myself.
and here is how i would test:
put the charger in connected with a seperate external AC cord at the lot or at home (assuming you can get it there), and see if you have noise being generated right out of the charger. for various reasons.
put about a 50watt Incan light bulb on the AC converter, and see how much noise it gives when doing its conversion. the quantity of noise (often) is relative to the quantity of current being drawn on the device. unlike switching electronics the bulb would be flat resistive, and provide for a control.
Bring a seperate battery that is not tied to the system, and run the inverter off this seperate battery for testing.
That give me many clues:
Is the RF being transmitted/aided through the cab wiring
is the AC converter really noisey when doing real work.
does the charger itself mess with the radio frequencies your on, when getting normal sine wave.
is the converter and its often very poor simulation of a sine wave assisting the chargers pulsing and switching in creating more harmonics and noise.
Is the converter reaching full voltage, as many converters dont output a full sine, they also dont output the full voltages, how bright is the light compared to being plugged in normally.