You say :
"during the Old Kingdom The Giza plateau was subject to a transition phase between the wet period from before and the arid conditions from after the fifth Dynasty and on. In this transition period, heavy seasonal rains would take place, which could account for the water run-off erosion we see on the Sphinx. A Pre-Dynastic dating is not necessary though. "
The "transition" period of the 5th Dynasty, (2490-2330BC), is when you suggest that 160 years of rainy seasons were responsible for the water erosion. IMV they might have been responsible for just some of the erosion. But, there is no evidence to say that such seasons would have been responsible for all of the water erosion.
On papers -
I am unaware of Paul Heinrich having published any papers at The Geology Society Of America, either. Presumably, such a venerated and highly respected scientific institute are not best pleased to be described in the manner of the article which you attribute to Paul Heinrich.