In defense of the arc type protractor, the converse of your criticism of it is that if the P2S distance is not precisely correct, the arc type will tell you that, and you can fix the problem.
If the tonearm is 1mm too far and you mount the cartridge 1mm forward so that the overhang is correct, can you really tell the difference between an arc with radius of 270mm vs. 271mm? The difference is going to be tiny. Notice that this is different from having the tonearm mounted right and having the overhang off by 1mm.
The good news is that the effect on the tracking distortion is also very tiny, shifting the null points by less than 1mm if the tonearm is 1mm too far or too close but overhang is right:
http://www.vinylengine.com/tonearm_alignment_calculator_pro.php?arm1=Arm+1&l1=ps&a1lv=271&am...