Try using a contrasting, commonly called a pop, color as sashing and/or border. A white on black print, or much darker color of one of the ones in your blocks could be what makes all the colors act nicer together. Google Quilted Table runner with sashing and you will see many examples. You could float your blocks by putting a sashing between them and use the same color as a border.
Tip: Take 1 each of your blocks to a fabric store and lay them out on the fabrics you are considering. And don't be afraid to be try colors you think won't go with them.