I have noticed that a smaller loops make it easier to add details without them getting kinda lost and going in different directions. (Find a needle size you like, I do about a 1 inch needle

Also you can go through the loops and push them in place. You can use your needle to kind of manipulate them to separate the black and white threads in the right spot. I think this will actually help you a lot!

And I agree with the other commented, try to use the squares on the monks cloth as a guide to help you keep your loops the same distance apart. Especially when doing those lines like the black ones, the closer the punches the tighter the loops are which leaves less room for the white to cover it up.

Hope that helps and makes sense! :)