Voltage difference is probably due to a voltage regulator (remember drops a volt to run it). Car adapter says 5V 2.5a, and we KNOW it doesn't draw 2.5a - or maybe it DOES when it's CHARGING.
I have a similar problem with my Sony GRT-100 laptop. Internal battery is 14.8v/4000mAh. External input is 19.5V/6.5a. Can't find an external battery to run it in the field. Thinking of hacking the case and going direct to the internal battery hookup, but I got a 2 year extended warranty on it, and I think adding a DC plug and wiring mod to the case would kinda void it...
Rick