What a fun fast project. If I understand, first I would separate out my whole squares and put them aside. Then I would cut my sashing rectangles from the remaining squares.
I would put the rectangles together along the short sides making the full horizontal rows of sashing. In your picture that is 11 rectangles long. Then I'd piece the remaining rectangles into 3-5 pieces at a time cutting them to the proper block height. You can do it in a loop even, but you only want to do about half the pieces that way. Then you take the left over trimmings and add them into mix so the fabrics are slightly offset. At least that's how I would do it, you don't want too many seams per sashing bar because you only have so much fabric.