The "lace Bronson" (horizontal weft floats) and "turned lace Bronson" (vertical warp floats) are being used to put the thicker pink threads to the top side of the fabric, to accentuate the windowpane check. I find it interesting that where the two lines of lace intersect, there is a little area of plain weave.
I omitted two picks before and after putting in the weft stripe, and I think it looks better this way. Compare the intersection in the top of the photo with that at the bottom. The one at the top is woven according to the original draft. The one at the bottom omits the "extra" pick between the blocks in the treadling sequence, and omits one of the two picks on either side of that "extra" one. So instead of adding a pick between the blocks, they are "sharing" a pick instead. See how the plain weave area looks more square in the bottom intersection, while the top one looks like a vertical rectangle.