I would personally go with a green that most matches the green as that is in almost all your squares..purple is in some.. and the green might help tie things down in a calming way? more traditional looking. The dark purple could work but what you could do is take that purple, place the other colors on top of it say leaving a sashing width size swatch of purple showing and take a pic.. stand back and look at that pic with your eyes squinted.. it blurrs your image but not the colors and your eye will pick out MOST of the time if its a good match or if its off.. sometimes I think something matchs to stand back give that a try and think oh heck no..
I vote for the greens (for everyone wondering how I know the colors looked at her profile and her postings and its right there listed Practice squares or quilt..