Sorry to enter the discussion late.
There is no doubt in my mind that the stamp is false. The way the circle was added to create the R part of the monogram does not match any of the genuine stamps I am aware of.
Regarding the host coin, I am uncertain the coin is genuine. The only way to tell is to do an XRF test looking for Gold in the alloy. I have seen several 1744 8Rs that conclusively tested as modern silver copies which look about as good.
I would focus on the edge design and the overlaps. In 1744 the Mexico City mint had not matched the edge die length so that the overlaps should be easy to spot on a high grade coin. The overlaps must be precisely the same length and they must be 180 degrees apart. Second I would ask to see an in focus picture of the lotus design. Even blurred something seems off.
Regarding having NGC
authenticate this coin, I do not believe they will do any more than a visual inspection of the surfaces for the base fee. They will most likely encapsulate the thing. For this coin it is a waste of money. Typically NGC
does not even weigh the coin unless you pay extra. They may now also do an XRF test but it will cost you extra and it will probably use a 20-30 micron deep hand held unit. A Laboratory level 100 micron or deeper XRF test would be far better and more accurate for authentication.
I may sound very negative, but after many years of authentication I would say that 8 out of 10 Pillar Dollars of this type that I have encountered prove to be forgeries when tested scientifically.
No one has asked - where did this coin come from?
I would guess the counterstamp was applied in Spain by the notorious group of forgers we all know from the last 10-20 years on eBay. They are the ones that created the printed booklet I illustrated in my book on counterfeit 8Rs. This source typically uses genuine cull coins or forgeries as hosts. This coin is not a cull. So if it comes from any of the names associated with the forgery ring I would change my opinion to completely bad.
Finally did you notice the verdigris on the reverse? That always puts me off when I see it on the reverse of counter stamped coins because underlying copper can be exposed by the application of the c/s.