I have figured out quite a bit in the last 24 hours regarding car mode, however my information come from playing around with the verizon varient. Maybe it can help though.
1) Car mode is definately activated by a magnet as apposed to an NFC tag as has been suggested. About 1" down on the left edge of the screen is the sweet spot (front and back of phone). The polarity of the magnet determines if it switches to car mode or flip case mode (that is, flip the magnet over and it will activate the other function or don't flip the magnet and move it from the front to back of the phone).
2) The navigation button only links to verizon's navigation software (which I have disabled) and does not prompt for an app to choose. I even tried installing a 3rd party, non-google app and still no dice. A work around for this is to open the map (which links to google maps) and search for a location to initiate navigation.
3) Once in CarHome, there is a setting to have car mode activate when connected to a selectable bluetooth device (must be connected to choose it). This would seem like a great opportunity to be able to use car mode with no dock at all, but... when trying it, car mode did activate, but it immediately closed. I figure either LG or, more likely, Verizon modified the app or has another service to shut it down to force people to buy the dock.
4) I modified a bracketron mount I had to locate a magnet in the right location to activate car mode. I used a tiny magnet that came off one of those pushpin looking magnets.
5) I installed a third party app for the car mode and when I place the phone in the dock it does provide a choose app list, so this is a good thing. If the other varients don't have the specific stock app, they could still have the service running that would recognize the car mode activation and prompt to use the 3rd party app.
6) Some people have suggested that car mode is not available in jellybean 4.2.2, but what the case is is that previously in car mode the home button would return to car mode, but now the home button returns to home. This presents an issue with the stock app because it doesn't show up in the recent app list, so the only way to get it back is to pull the phone from the dock and put it back in. The 3rd party apps show up in the recent app (and can be launched from the app drawer for that matter) so this isn't an issue in this situation.
Think thats is about it. Don't know if the right people will look at this post, but it would be nice if people smarter than I could figure out how to make the navigation button allow selecting other apps and also how to prevent the activation by bluetooth from closing out. I know there are other options out there, but the stock app is simple and the processes are already running on the phone so I don't need other apps eating up battery. I also have a GPS sitting right next to it, so I don't really need it to be trying to maintain a GPS lock constantly like other apps do.
Hope this helps.