Someone (Peggy P.?) suggested perhaps using black inside the squares and I thought perhaps that might work well. I'm going to check my stash for black or very dark blue fibers in various textures to make up the 9 combinations I'll need.
Jane C. used a thicker thread but it's not a vibrant and she used satin stitch for the borders so they're less prominent. (Hopefully she'll edit this and add a photo of hers.)
I got another surprise when I began stitching with the Watercolors--I used it to select my other colors and looking at the skein while in the store I didn't see any blue in the fiber at all. I bought purples, russets, and a bit of pale green. When I began stitching all I saw was blue. I cut the thread to deemphasize that and I pulled some blue pearl cotton from my stash to add to my fibers. So, learn from my mistake: Don't forget to untwist the skein you're using to select your other colors and walk it to a window to really see the colors in it.
The inner braids are one thread wide, the inner dividers two threads wide and the outer border three threads wide, all pretty much with the same overlapping cross stitch braid pattern.
On the left I used one strand of Needle Necessities overdyed thread. On the right I used an unknown silk (I'd lost the tag). It has seven strands. I used one strand for the narrower borders but tried two strands for the widest border and liked the coverage I got.
The pattern called for Kreinik #12 braid but I don't have much so I used a random piece of silver (it wasn't much fun to work with, whatever it is) on the pastel piece and Kreinik #8 gold braid on the red/green one. #8 is a bit skimpy. So, when you're picking your colors, be sure to get #12 braid for your metallic.