I've come up with something that lays relatively flat but still looks similar to LiriGal's bracelet. I also wasn't happy with the plain edge on LiriGal's so I embellished mine. I'll try to describe what I did below. I added numbers to LiriGal's pattern so you'll know which steps I'm referring to.
STEP 1-6: Make as directed by LiriGal's pattern. After completing step 6, I wove back around through the netting and popped out the center bead of each arch by skipping that bead. That creates neat little points.
STEP 7: Do this step as directed but weave back around each picot a second time, skipping the center bead. Doing this makes those little crosses of beads more stable.
STEP 8: I won't make the clasp loops as she makes them. I'll come up with something that I like better when I make a bracelet. I skipped the 4 bead netting that she adds on each corner of the bracelet and also changed how the rest of the netting is added and only used 3 seed beads instead of 4. Instead of adding it between the center points of the picots, I did it more like Michelle Skobel's pattern. So, I wove around so that I came up through a left bead of a picot, picked up 3 seed beads, then went down through the right seed bead of the next picot. I repeated this all the way across on both sides.
Next, I wove back around to the netting I just added. For each trio of netting beads, I went through the first one, skipped the middle one and went through the third one, popping out the center bead to form a little point.
You can read more about my experiments with this pattern HERE and HERE. The beads that I used in my tweaked sample are Miyuki 11/0 seed beads "Dark Bronze (11-457D)" and 4mm "Peridot Twilight" fire polished beads.