Best Action Cam for In-Car Track Recording

[cib24]

I'm looking for an action camera (or two) to record my track days in a minimum of 1080p60 but can't figure out which cameras on the market meet my requirements. The camera will be mounted on the rear anti-roll bar in my Mazda RX-7 and in the future I may get a second camera to mount on top of my steering wheel column pointed at the gauges. What I would really like is the following:

1. 1080p60 minimum

2. image stabilisation to avoid unnecessary shaking as seen in the following videos:

https://www.youtube.com/watch?v=7Ykx3hlJQrg
https://www.youtube.com/watch?v=W3LSNHYvKMg

3. As long of battery life as possible, and if not possible then ensure it is easy to change batteries

4. No fish eye effects.

Ideally I would sync these up to an app like TrackAddict or Henry's Lap Timer.

The market is flooded with cameras from the GoPro's to the Sony's to the Garmin's and TomTom's but what are you guys using?

Thanks.

[cib24]

The GoPro's don't have image stabilisation though right? So, the videos might have nice details but will likely look shaky as hell?

Or perhaps I'm thinking about it the wrong way and there is a mount that sucks up a lot of vibrations and movement?

By the way, I meant the rear strut bar which you can see in this photos is covered in plastic at the top of the back of the rear seats.