Hi Kevin,
The 1 SOL 1876 Y.J does exist !! But it is a Pattern, as Krause states correctly in it's 1986 edition under # PnA24.
Without beeing conclusive, researches done in Peru an in the USA, show that it was probably minted at the Philadelphia mint. I don't know how many pieces. Due to financial and political problems in Peru in that time, the coin was never mass produced (there is also no 1877 1 SOL !!) .
The only specimen I know belongs to a peruvian private collection, which I was lucky to see by myself. Compared with it's nearest "normal siblings" (1875 Y.J and 1879 Y.J) , this 1876 Y.J piece was coined on a more perfect flan and has more regular and finer designed details. Unfortunately I don't have any picture.
Hope this info helps you to (avoid) getting crazy
Best regards