For the OP
First... you have a doppelganger resemblance to my brother. Very freaky
I have the opposite problem, I can charge when driving, but not while off (at least with 3 batts at once

)
You need a very good inverter to charge Phantom batts in the car. You probably should not do it from the cig lighter, but from a hard wired connection. I have been doing it from the cig lighter. But after just blowing a fuse while still letting lots of magic blue smoke out of the inverter... no more.
I just bought an inverter that I can hard wire for Phantom batts. It also has a swapable cig lighter adapter that I can use on road trips for the laptop etc. I haven't tested it yet, but it is a quality brand. When I do, I'll post good, bad, or, ugly