I like to make it wonky on purpose. That takes the pressure off being perfect. But I have to be careful with checks. Some can make me dizzy,

I saw a picture of appliqued fruit on background squares of black and white checks. Each block was one pear, apple, etc with the leaves. Thought they were really nice. Because you put a border around each block, won't have to match up anything.
Carol B

I purchased some of the black and white checkered print fabric several years ago. I used it to back a twin quilt for my race fan. Afterward the the left over fabric I used to make a large roll pillow that is used at the top of the bed.
It has held up rather well.

I have some good black & white check fabric that isn't wonky; haven't used it yet, But I think yours would be cute to applique on it with primitive style designs, nothing complicated and let the wonky just happen. Sash with complimenting solid colors and just sail away with it. I love creating as I go along. We are artists aren't we?

Thank you, ladies! With all these great ideas, I can now justify to myself buying that checkerboard fabric!