Great, we now agree on that.I totally agree about the first part: "ratio of resolutions is inverse ratio of two numerical aperture values".
The word, "corrected" for aberrations , well, now we are talking about engineering, making modifications to a simple lens.The words "reference sphere" are important, and are related to a footnote by Kingslake in his "Optics in Photography", page 107. You can see that page in its entirety HERE. The key thing is the footnote:
It is a common error to suppose that the ratio of Y/f is actually equal to tan θ', and not sin θ' as stated in the text. The tangent would, of course, be correct if the principal planes were really plane. However, the complete theory of the Abbe sine condition shows that if a lens is corrected for coma and spherical aberration, as all good photographic objectives must be, the second principal plane becomes a portion of a sphere of radius f centered about the focal point, as is correctly shown in Fig.6.2. In this case, Y/f is equal to sin θ', and it is evidently impossible for any lens corrected for those two aberrations to have an aperture greater than twice the focal length. Thus, no well-corrected photographic lens can have a relative aperture greater than f/0.5.
It is this observation by Kingslake that explains why NA_wherever = 1/(2*Feff_sameplace) is an exact relationship, and not an approximation that is valid only in the limit of small angles.
And no, tan(theta) is not same as sin(theta) when dealing with extreme conditions, like focusing to infinity. The very fact, using your equation 2, when m is approaching zero, you are saying the effect of wave optics is infinite, That is wrong, with your modified lens or not. Period!
For the rest of your argument, I think you are not recognizing the fact when we speak of spatial frequencies, we are dealing with segments, not a point and the ratio is determined by those two red segments, which make it independent of magnification.