Pretty much as expected, the cheap craft adhesive sheet turned out to be inadequate to the task of holding the thin upper border ring onto the clutter collector:

So I stripped the adhesive off with naptha and arranged a cut in a 3M 300LSE acrylic adhesive sheet:

Four small tabs held that ring to the central piece while I stuck the acrylic ring on it, which turned out to be easy enough. Then I cut the tabs, peeled the paper off the other side, stuck the ring to the plate, and it’s once again ready for clutter.
The bond is visibly better when viewed through the top of the ring, so I think the 300LSE adhesive is thicker and gooier than the craft sheet adhesive, which isn’t surprising at all.