I am getting there. Rather than trying to recombine the polys I made my box with 9x9, then manually selected the outer 2 rows of faces on all sides and did a linear subdivide until they were small enough to match the ball poly size (or close enough).
Then I did the boolean and this looks really good:
https://drive.google.com/open?id=0B3P6IntD-KkaTHlzQi12UVVQZFE
Then I did the boolean and this looks really good:
https://drive.google.com/open?id=0B3P6IntD-KkaTHlzQi12UVVQZFE