Pub User, interesting point, but I wasn't sure that "pilot supervising co-pilot activities" is an accurate description of a safety pilot. So I had a closer look...
I noticed "pilot supervising co-pilot activities" is case F(ii) in that LASORS Appendix, and it does say to log P2 time.
However, further down the list is case N: "Pilot acting as safety pilot". This is supposed to be logged as SNY time in a spare column and so not added into your total time.
So the next question is, what exactly is "pilot supervising co-pilot activities"?