I did some experiments and so far haven't figured it out.
BTW when I said "big caps" I didn't mean really giant.
[fast forward a few hours of fooling around trying various capacitors, indoor/outdoor tests etc]
I tried adding 1uF caps (ceramic, low ESR) right at the camera boards, both on the power feed to the cameras as well as on the third battery terminal. Neither seems to have had much effect, or both at once. Maybe slightly improved, but still bad enough that it is hard to judge. I took a closer look at the camera PCBs too and they have quite a bit of input capacitors on the power line. At least 3 or 4 fat 1210 sized SMD caps. It is definitely a noise issue since it only happens when the cameras are being flown on my vehicle (a multicopter). I did double check this to make absolutely sure just now. I also can't even replicate it with the vehicle running on a test stand (which is highly strange). Maybe it only occurs at short exposure times (it is brighter outside)? Also tried higher ISO inside on test stand (exposure times similar to outdoor flights)... no bands.
Just took it outside to take some photos in bright sunlight, even when on the ground... BANDS! Maybe this is some kind of light leakage? The lenses are de-cased, but are also facing downwards and sitting on the belly of a vehicle. Sounds like I am getting somewhere finally!