If I understand the problem correctly, when you cut the squares, you are cutting off part of the logo? if that is the case, I would change the shape of the square to match the fussy cut. I don't know if you could still use your quilt pattern or if it would need to be changed too. I think Warm Wishes would work well because you can make the fussy cut any size you want. You could appliqué something over the problem but that would probably not go with the pattern? Good luck, maybe someone else will have a good solution for you.