Somehow, from that maze of confusion, the designer, who should be sainted or knighted or at the very least be gifted a lifetime supply of warm cookies, responded quickly and clearly:
Oh how I wish we could just sit down together for a minute or two. It would be so much easier than trying to explain.
Well, here goes. If this still doesn't make sense, we can try again.
In the pattern, one circular needle is the instep and the other is the heel.
The easiest way to convert this to double points is to use two needles for the heel and two for the instep instead of splitting it into thirds like you have it. With four double points you can pretty much follow the pattern as written using 2 dps = 1 circular.
A second option using three needles, when you get to the heel, put the heel stitches on one needle and the instep stitches on two needles.
The purpose of the 31/29 split is to center the lace panel down the instep of the sock. Knowing that should help you figure out stitch placement.