So the list is:
A 16-35/2.8 is likely to be similar in cost, weight and issues to the current one. It would also be more expensive than the 16-35/2.8 II if it fixed sharpness/field curvature.
A 17-35/2.8-4 is likely to be similar in weight to the existing lenses and priced somewhere between the 17-40 and 16-35. If it doesn't fix the field curvature problems (which I'm hoping it will due to variable aperture) and corner sharpness then it may as well not exist.
A 16-35/2-2.8 will cost and weight more than the 16-35 but it may fix issues to do with field curvature and corner sharpness. I have trouble seeing filters work easily with this lens.
Though it would be wonderful if true I do not believe any improved lens will be even close to the current pricing. Canon has been raising the prices of their improved products by 50-75% over the old price so i would expect the 16-35 f2.8 III to cost about $2300 and if there was a f2-2.8 version that would probably be closer to $3000. Our only hope is the 17-35 f2.8-4 that may "only" cost $1600 or so but if it had good corners and distortion I would be happy to loose the stop of light on the long end.