I scanned the responses in this thread and didn't see this, but forgive me if I missed it.
The issue with net loss of battery life during heavy use in the car is related to both the amp rating of the power adapter, as well as whether the adapter is a dedicated charge port, which is part of the USB charge specification. Obviously, if the adapter is rated for less than 1000mA, the max the One will draw, you won't charge at maximal speed, but getting an adapter rated for more than 1000mA shouldn't make any difference, so long as it's a dedicated charge port. DCP shorts out the data transfer pins, signalling to the device that it can draw more current, whereas non DCPs limit current draw to 900mA. One would think that a car power adapter would be a DCP because it obviously has no data capacity, but that seems not to be universally the case. The easy way to tell is to go to the stock power screen from settings while plugged in. If it says charging - A/C, it's a DCP and can draw up to 1A, if it says charging - USB it's not a DCP and will draw less.
I can vouch that with the proper adapter you can run as much as you want and still charge. I use the HTC car dock, and have nav running, the screen at max brightness, streaming music both from the cloud and to the stereo via bluetooth, and it still charges. It gets hot, but it charges.