I'm not sure I can explain this right but this is the way I did it. On the right and left of each block, I put a black sash on, then sewed the four big blocks side-to-side to make one long row. I then sashed all across the top of each row (4 rows in all). I put one last sash on the bottom row, then added a blue border all around. I didn't QAYG anything but the blocks and it turned out fine.
I just got to thinking....I made my black strips for sashing at 1 1/2" so there is only a 1" sash between blocks. Maybe that is why it didn't matter if I batted them. Who knows? :)