Well, I ordered a Xiaomi Yi. It seems to be as good as a GoPro Hero 3, which is good enough for my needs. It even does 1080 at 60 fps and 2K at 30 fps.
I'm still considering whether to get a helmet mount or a handlebar/seatpost mount. Maybe if I place the camera on the seatpost it will deter some drivers from getting too close to me?