For the most part, cheap inverters are noisy. While you might not hear it on 2 meters, driving by any truck stop listening to any HF frequency will give you an indication of how bad they really are. High quality, well-filtered ones, aren't cheap, which adds some insult to injury.
While this isn't the answer you're looking for, I believe I'd take a different approach. Either I'd buy a laptop that could be powered directly from the vehicle, or build a charge pump to boost the 13.8 up to the 18.5 or what ever.