The Sony a7S does not record 4K, at least not internally.
you would need an external recorded which bump up the costs and complexity considerably.
as for the GH4, it's a solid camera.
a friend of mine have one, I'll give your idea a spin on the weekend.
take into account that moving fast means rolling shutter and motion blur,
as well as a small angle between frames. you might need to drop frames.
I think that the GH4 burst mode (12 FPS for RAW & 40 (!) FPS for JPG @Full 16MP) would be a smarter move.
Cheers.
Avihay.