I am fascinated by the plot arc of this thread, Sterling. FWIW, I used to be an avid "statement necklace" person and, somewhere along the way, they really fell out of favor for me. I do still wear necklaces, but they're more often simple pendants or geometric shapes than large statements.
Perhaps what you're looking for, rather than a statement item or a "third piece" is a focal point for your outfits? That can be different for different outfits. I have a small library of these types of pieces... an interesting belt, a hat, a few necklaces, scarves, a bold tote, a cuff, a unique pair of shoes, a kimono topper, etc. These are heart pieces rather than head pieces.