The apparent fringing capcitance will change. Since you have phase change linearly with frequency, I think that is why you have such a big C1 term. In my experience, the phase vs freq should have a very small shift, perhaps 5 degrees at 6 GHz. The capacitive polynomial doesn't account well for delay, and since you phase vs freq is nearly linear, it means you still have some effective delay in your result. As you point out, fringing capacitance cannot go negative (become inductive) so if you phase vs freq goes past 180 degrees, you MUST not be accounting properly for delay. Add delay until you phase vs freq is flat, and phase just does not quite go positive anywhere, then compute you capactive polynomieal.
ripples on a long-line short (I recommended short, not open, as opens can have some radiation that confuses things), will give you a combination of goodness of c0 and load. If you have a bad load, it will set a baseline ripple, if you have a bac c0, it will add to the ripple.
very simply: I recalled the S1P file into the PNA. I put up a phase trace. I put up a marker and hit "marker:marker functions: marker>delay" then I moused over the marker and right click to get the Marker... dialog (also available under the soft keys Marker, Marker Properties) and I changed the marker default to be G+jB, which is the readout for the the inverse smith chart. And plotted the first plot. I then hit "save data as S1P" to save data.
Then I set the delay (under scale:electrical delay) to be 66.7ps*2 (if I used port extension, it would automatically know it is a reflectiona and do the times 2 for me, but electrical delay doesn't do that), Put up a second marker, did the same thing. And plotted the second plot.