At first I liked the idea of cutting them and rearranging, but so many are so offset if you did that you would have to reduce the size of the squares to a common low denominator that would allow for cutting the circles and getting enough of the circle in each quarter.
If you don't cut them apart I would put the darkest square in one corner and "ombre" the rest so the lightest is in the opposite corner. If I were adding another color I would go w/ white since you are wanting it modern. (or mimic the "ombre" effect in the sashing w/ more blues) On my screen it doesn't read autumn.