Why not an enlarging lens or a process lens?
Per Nikon's propaganda, the 105/5.6 El Nikkor is optimized for 2x - 10x enlargements (as a taking lens, at magnifications from 1:2 to 1:10) and on 35 mm film will give no distortion, is apochromatic, and should suffer minimal vignetting. Manual aperture, so no issues with framing rate. But probably not the best taking lens at infinity. Rodenstock offers Rodagon-G enlarging lenses that would be better for use at infinity.
Process lenses, e.g., Apo-Nikkor, Apo-Ronar, Apo-Artar, Apo-Saphir, have very low distortion, are highly corrected for color, are very sharp, and most work well at all distances. The ones I named are used by demanding large format photographers at all distances. In most lines the shortest is 150/9 or f/10 but if you need 135 mm or even 100 mm those Apo Saphirs will cover 35 mm. Manual apertures, again. Of these lenses, only Apo-Saphirs are hard to find.
It is possible to make a lens with absolutely no, even less than no, falloff of illumination off-axis, but most readily available lenses lose illumination as cos^4(theta). The longer the lens, relative to the format covered, the smaller theta. If that's what you mean by vignetting, you want the longest lens you can use.
If you want good performance at distance, an Apo-Nikkor or Apo-Ronar will do you very well.
About fitting a Nikon body. Why do you insist on AI or later mount? Adapters from, e.g., M39x1 to Nikon F exist but are scarce. They can, though, be cobbled up, and
www.skgrimes.com are fine cobblers. If the lens is long enough -- why are you willing to use such a wide range of focal lengths? -- using a bellows for focusing is a viable option.
About framing rate concerns. Silly. The diaphragm actuation linkage can always be disconnected. Nikon and Canon lenses made for 35 mm SLRs are used by "Hollywood;" as adapted to cine cameras have manual diaphragms.
Finally, what are you trying to accomplish? Not to be impolite, but your requirements read like something dreamed up by a physicist that thinks it has unlimited funding. In other words, its a pretty silly wish list.