Most "Moon Cactus" use a Hylocereus as the recipient plant. Hylocereus is Dragon Fruit. But grafting isn't as easy as you might think. You say you are a cactus noobie but have you done any grafting?
Before you do anything else, though, did you water after you repotted into a larger pot? Did you take all the old soil off before repotting? How big is the larger pot? Is the soil very damp a week later? Are those dark spots squishy? Dry feeling? Can you rub them off with your finger?
More photos of the pot and soil would be helpful.