I've not made it, but looking at the pattern (its gorgeous!!) the only way I would be able to keep track of the squares is to use a design wall.
In fact I would cut the pieces in the order in which they appear in the quilt. Cut all the pieces for the first vertical color and place all of them on the design wall - leaving room for the pieces you havent yet cut. Then I would cut all the pieces for the first horizontal color and place them. Continue with a vertical, then a horizontal color. By doing it this way you are always filling in the squares from the upper left corner down to the lower right corner, minimizing the number of "blank" spaces you have to leave open for uncut colors.