[Brightcolours]

Your post is confusing. You say that to have no focus breathing it needs to shorten focal length (correct), but then you say that is unacceptable to you because it changes perspective. 

 

If you talk about perspective as it is talked about in art, that actually changes when FOV changes.

If you talk about perspective as in point of view, it will not change, either with focus breathing or shortening of focal length.

 

As for your calculations, they still do not make sense (well, the outcome you typed). Version 1 of the Nikkor 70-200mm f2.8 VR has a narrowing FOV towards MFD. Your post just above seems to assert that that changing FOV will mean a longer focal length.

 

Also, for a single lens calculation you still need to know the front nodal point to judge the subject distance.

 

And yes, to have no focus breathing, one has to take care of that in the lens design. That is why specialized film lenses which have low to no focus breathing are very expensive.

 

About that Nikkor 70-200mm f2.8 VR:

1.5m MFD, max. mag. 0.16x

Taking a 1.3m object distance (assuming a single 200mm lens), gives a focal length of 179mm.