I like the idea of off setting the columns. Move the second and fourth columns up by half a block, and take the odd half heart block off at the top. Then fill in those half block spaces at top and bottom with more black and white checkerboard fabric. I think the design would look more interesting than the lined up columns and rows, too.
Some block designs can't merely be "trimmed" without running into the problem you have. In those cases, I would make the block smaller by taking in seams, rather than cutting off at the edges.