I think PCGS is crazy. I looked at the images of the reverse on my laptop (so I could pick it up and rotate it clockwise 90 degrees) so I could see it in an up right position. Once I did that I could clearly see that it the reverse style of the Liberty cap or Draped bust cent and not the style of the Birch cent. Also when you do that you can clearly see the 1 in the numerator of the fraction and the words ONE CENT in the wreath. The 1 is below the left upright of the N. On the Birch cent it is below the right serifs of the E. Also J-1 is a silver center cent and ONE CENT is smaller and more closely spaced than on this coin. I don't see a silver center plug. J-6 is a white metal piece which this also obviously isn't. I still think this is a heavily corroded 1793 - 1807 large cent. You asked for thoughts, there you go.
I agree. I also enlarged the reverse image and where you are identifying "top of G" and "star" as well as "W Left leg" are all clear to me to be the ending of "America". This debunks it being what you are hoping to think it is. It's just a large cent that's heavily corroded. Caesar was right, people believe quickly what they wish to be true. As for PCGS, they neither confirmed nor denied it being anything. The clearly said no service and returned. On the slip they returned was just what you had written to them. As for J-1 / J-6, typo/miscommunication. Nothing more.