Good info, but the setup you describe isn't quite what myself and a couple others are thinking... Remove the inverter entirely from your equation. What are you left with? A UPS that will run until the tiny battery dies, right? Now remove the battery. Then take the leads that previously ran to the battery and hook them directly to your car's battery. Now we have a self-filtering, alternator charged, hopefully uninteruptable 12v DC to 120v AC solution!
Or so goes the theory. Testing begins in about two weeks for me...if anyone gets to it sooner, let me know!