Because there is no numerical overlap, I have placed the listings for both Moore's Alley and Moore's Court on the same page, though it should not be taken as proven that they were the same place.
(1785) #1 Moore's Court, Dill, Adolph
(1785) #4 Moore's Court, Moss, Isaac
(1785) #5 Moore's Court, Martin, Jacob
(1785) #6 Moore's Court, Pompey,
(1785) #7 Moore's Court, Weymouth, Margaret
(1785) #8 Moore's Court, McIntosh, Daniel
(1785) #9 Moore's Court, Fitzgerald, George
(1785) #10 Moore's Alley, vacant or residents would not give name
(1785) #14 Moore's Alley, Shoulder, Martha