So I've laid out all the squares, in the order I like them. I followed the Sudoku principle, so no color appears more than once in any row or column:
Some of the greens are clumped, but I didn't want to have to rearrange it, because shifting one meant shifting like all of them probably. I love the middle row with the solid blocks.
I've started the actual assembly, by rows. I figured it would be easiest to use the tails to attach the blocks down the long sides, then use extra yarn to sew across rather than down. It's reeeeeeeeeally hard to keep them even though! You can't fudge the edges much to make them match, and since they're geometric squares, you can really tell when they don't line up. Granny squares are a lot more forgiving. But uglier. So there's the tradeoff, I guess.