70-200 F4 Heavy Breather?

That's not correct.  For a given image circle, if the focal length remains the same the angle of view will remain the same.

What can happen is that the image circle decreases to the point where vignetting occurs, but this is far from assured.  In fact, with lenses which focus by extension the opposite occurs -- the image circle becomes larger with focus.

The approximate formula to calculate focal length from distance and magnification is fairly simple:

F = (D * M)/(1 + M),   where F= focal length, M=magnification, and D=distance

The problem is that "D" in the above formula is from the optical center of the lens to the subject, whereas Nikon specifications give the minimum focus distance from the film plane.  While it's certainly possible to compute the optical center of a lens from a detailed enough description of the design, as I noted above I lack both the data and the math to do so.

In fact, Thom and others measured the maximum focal length of the 70-200mm VR1 at MFD at 182mm.

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I miss the days when I used to be nostalgic.