It is very easy to keep your blocks aligned when using sashing strips, even if you don't use cornerstones.
Create your rows as usual, with a sashing strip between each block. Add sashing to the bottom of your first row of blocks. Turn this row to the wrong side and using a pencil and ruler, mark every block seam on the wrong side of the bottom sashing strip.
When you add your next row of sashed blocks, pin first so that each new block seam aligns with a mark on the sashing strip. If you have a little excess fabric in a block, ease that block to fit the sashing. If the sashing has a little excess fabric in it, ease the sashing to the block.
The pencil marks take the place of cornerstones so that when you are finished, all of your blocks are lined up from row to row.