High-density, light multiconductor cable: sources/suppliers/manufacturers?
I might be barking up the wrong tree here, but if you've got any extra space at all at the far end of the cable, you'd probably do better to digitize the data there. You can then use a robust signaling method over a single conductor pair to deliver the data upstream. Coaxial antenna cable can be gotten in really tiny diameters, it's very noise-resistant, and can be quite strong.

Most of the major analog IC manufacturers sell multi-channel serial ADC chips that you could trivially integrate (again, assuming you have space).