Love these fabrics and you look to be off to a good start- I think you're smart to lay it all out like this and just keep moving blocks around til it feels right to you- love the solid four patches mixed in- its a happy design:)
Have you tried converting your photo of the blocks to black and white? Then you can look at how the light/medium/dark values are distributed and play around with that.
Do you think the "busyness" you're seeing could be because the blocks are laid out on point? I wonder if squaring them would solve that for you.
First yes, convert to black & white as Terrysim suggested and use the b/w photos to get your values a bit more evened out...that will def help your eye to see your 'colors more separated'.
Second, the busyness you're seeing when looking at this.... Two solutions, either the plain squares you mentioned or some sashing could cut that back. If you go for the plain squares, just follow the pattern you linked that was your original inspiration! :) Put your plain squares where the appliqued flowers are in the pattern. If you want to try the sashing, just unfold some yardage of your solid and lay out the blocks on top of it leaving some room in between to let the 'sashing' show.....allows you to see what it would look like and gives you a good visual without having to cut into it. ;) (you could also do this to see if you like the plain squares!!)
It's a nice pattern and great fabrics/colors....it's going to be lovely when you finish!
I would try just putting plain squares in randomly. But I would consider using plain blocks of colors instead of white. Just try moving them around where they look the best.
Cut out blocks of construction paper in various colors and play around with them. That way you have not waste time or material.
I'll echo the above comments about switching to black and white to get a good distribution of light and dark. I think this might work well with some sashing to separate things a bit.