I finally get it!

IME that is a serious oversite. High end analog is not at all forgiving to issues like this. Glad you got it worked out Slaw. 

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..

First and foremost, every time I see Phoenixengineering participate on this Board I smile. He is a great all-around guy and has a wealth of useful knowledge. 
Now that aside, as someone who gave up on VPI decks (three of them) and went to vintage decks on custom plinths and Reed 3P arms, I have learned from personal experience that P-S is not a demanding spec if you have a typical headshell that allows the cartridge to slide back and forth. I have learned from mounting my own arms that a tonearm's manufacturer's specified P-S may not allow for all modern cartridges to come into optimum alignment. You may argue that this is the fault of the tonearm manufacturer but such is not necessarily the case-often it is due to the cartridge manufacturer having an unusual stylus to cartridge body mount configuration. 
Case in point would be my current VdH Crimson Strad. When I mounted my 10.5 Reed 3P to the spec'd P-S, I could not move the cartridge far enough forward to get to the Lof B on my Feickert alignment grid. Remounting the arm a few mm's further away from the spec'd P-S allowed me to the to that point. 
Brian Walsh of ttsetup.com confirmed that what I had done is the only approach and that it does not, in any way, compromise performance-he was able to accomplish optimum alignment with his very sophisticated software based tools. 
So imho HW is correct that being a mm or two or even three is not a problem if the stylus can get to the desired point given your alignment type/choice. To put it slightly differently, the stylus does not know or care about the P-S distance. P-S serves as a range within which most cartridges can be optimally aligned within the slots. I have said this before and will say it again-the SME approach to P-S proves my point: no slots and instead the P-S is changed for each cartridge using their ingenious pivot point sled. 

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.

oldears has got it right. A 1 mm difference in pivot point can easily be accounted for by any protractor with the exception of the expensive "arc" ones that are adjusted to the theoretical distance rather than the actual distance.

Theoretics aside, I have always believed that the adjustments for horizontal tracing angles (for which there is no universally accepted standard--there are many and all are compromises) are obsessed over.  Not to mention the hundreds of dollars spent on protractors that give the same result as a $20 one.  Proof of this, I suggest, is found in the success of the Viv Lab Rigid Tonearm, a short arm with no offest.  Said to sound great.  Tube units measure worse and sound better.  Same with LPs and digital, same with belt drive over most DD.  The only test is your ears.

More important cartridge adjustments IMO are SRA (depending upon stylus shape) and especially azimuth.