Don't limit yourself to just GoPro. There are TONS of action cameras out there, and GoPro is not the best. They just spend a lot of money on advertising.

Their Hero Blacks are usually some of the best cameras on the market within their generation. If you're buying less, you should not limit yourself to the GoPro line because you'll probably be able to get a better camera for less money. You can even stick to the GoPro mounting systems and still be able to choose from a lot of different brands.

4 frames per second is kind of a bizarre requirement. Generally you don't get below 30 FPS on video, maybe 15. When you go to time lapse it usually starts around 1 frame per second and goes slower.

On video you need to stay away from slow frame rates because in low light it will increase the shutter speed to try to suck up enough light to make a decent exposure, and that will turn your video into a blurry, useless mess. You're better off capturing low exposure levels then software amplifying the signal. It'll be noisy but at least it won't be blurry.

I've owned a GoPro in the past, but honestly, it was pretty much the worst, buggiest camera I've had (out of over a dozen cams total). Right now I have a Contour Roam3 up front, and a Fly6 in the back. Mainly I want decent video quality and a long battery life. The Roam3 is borderline at 3 hours battery.