I also noticed you said there was a poor connection at the van's battery terminals.
A couple weeks ago, it was around -20C, and my battery wouldn't turn my engine over sufficiently. My brother hooked up his really heavy duty cables to give me a boost. Well, it didn't work, even after letting my battery accept a charge for a while. My brother's battery has those same crappy side screws, and a rad hose is right in the way of getting the clamp on properly. But once he persistently adjusted the clamp, and got a better connection, my engine fired right up.
So, the moral of the story is, you could try charging those agm's, from your vehicle, for hours, and achieve very little charging. Then you run them down over night, and then think it's your laptop, or maybe the freezer, or maybe ?????????, the following day.
Pretty much every reply has said you're overloading the system. But now you're gonna buy another inverter, without verifying anything. May I suggest you spend way less money on a multimeter, and go from there. Otherwise, you'll probably be starting another thread about how your brand new 1000w inverter won't put out either.