John is too far back.
The autosomal DNA tests can only test 4 to 5 generations back with any accuracy. This is determined by the amount of shared DNA getting halved in each generation as you go back.
Your parents are halved, your grandparents have one quarter, your great grandparents have one eighth, your great great grandparents have one sixteenth - and that is 4 generations (not counting yourself) right there.
So the autosomal tests can only test DNA accurately between 100 and 150 years ago - assuming 25 years per generation.
John was born and died in the 1700s. Which is definitely too far back!!
Edited to add - If Moore is your married name then you can never be related to John Moore. Your husband is related to him. However the DNA connection still wont show up - for the exact same reason I gave above.
PS thanks for the best answer.
The email says Sheppard-2686 - so thank you PIP Sheppard.