I have made many string quilts and I too spend a lot of time arranging and rearranging the blocks until I am happy (or as happy as I'm going to get) If I have a color (like your purple) in some blocks but not all, I look at each row and distribute them in the row and then look at the columns and again move them around again until it looks sort of evenly spaced out. In yous I count 27 with purple (not sure if this is correct but for my example I'll use 27) you have a total of 48 blocks. 3 x8 = 24 so I would put 3 in each row and then add in one more in 3 of the rows.one extra maybe in the top row and one extra somewhere in the middle and one extra in the bottom or next to the bottom. It dosn't really matter. I might start one row with a purple, the next row I would skip a block and randomly add the 4th. I would probably look at the stripe fabric as well. If I understand your numbering I mught move around #7 (made of 4 blocks) and #8 so that I didn't have the 3 purples all together but you probably only have to move the lower left one in #8 and switch it with the one below it (top left of #11). But really in the end it all works once it is sewn together. Also, even if you don't have a design wall, you might like to get a vinyl table cloth the kind that has the soft fuzzy backing ( they are really cheap, maybe $3 or $4) when you lay blocks on it they sort of stick and then you can roll it up when you have to move it and they stay in place when you are ready to unroll.