I finally get it!

Maybe I am naive or maybe someone could explain to me what the SONIC difference is between -1mm and +1mm S2P difference?

If there is enough space/play in length of the slotted head shell cart mount hole.
So you are able to get desired overhang and hit you preferred alignment type.

Then there should not be any SONICALLY difference between those two S2P distances.

It only become a problem if you can not reach the desired points for your arch protractor/overhang. So as I see it the slotted holes in the head shell allows some tolerance in pivot to spindle distance.

And we then fine tune it IF we use a ARC protractor that fix the overhang!

But yes you loose out if you use a tool that set the overhang by other suboptimal techniques.

As everyone understands now that a arc protractor has yet here another benefit when it adjust the overhang and in the process fixes any intolerances that just that specific TT and tonarm combination has! 

Every TT has a unique S2P distance because of their is always a slight mounting tolerance of ± X.XX mm. 

So please use a arc protractor and this P2S issue is not any issue anymore if you can adjust in the slotted holes in the head shell..

Exactly that I am trying to say.
Excellent idea to move the pivot point instead. 
So the spindle to pivot length is nothing to OCD about.

The just make sure that we can hit both of the points on a arc protractor without moving the protractor or turn the platter.

(If you do it by moving the pivot point or sliding the cartridge back and forth in the head shell just don't matter.)

And we are done with a alignment.

A arc protractor is free.
As downloaded SW and you put in your specific TT S2P distance.
And you chose what mathematical equation that you want (Löfgren A/B, Bergwall or ..)
Print it out, check distance of the printed result to ensure it is in scale.
Done.

As for azimuth I were one of them that obsessed to get my setup as good as possible. After reading people setting up with special test/calibration records. And with special equipment (fozgometer) or computer software. I also used digital oscilloscope and so on.
Read people that had many different pressings of Denon calibration records + other brands of calibration records. And they come to the conclusion that every single calibration record measure slightly different... And remember supposedly when making a calibration record they hopefully make all the angels setup on the cutting lathe as good as possible.. and we end up with variance anyway..

So should we set up perfectly against one calibration record? What is then the result.. .. that we only have a perfect setup on THAT record that mimics just that particular angle that the cutting head had when it cut just precisely THAT laquer..

So the lesson was azimuth vary from album to album. And if we suppose that the cartridge manufacturer has done as good job that they can do. Then it is just to put your cartridge for azimuth as horizontal as possible. And in a average between albums it will be the best.
(If it is not damage/faulty in any way)