I tried a slightly different approach with the button box. Since what I am looking for are small buttons, I reasoned that they might easily be overlooked in the wealth of buttons in the box.
So instead of rummaging through the box looking for likely prospects, I dumped all of them out onto the table and removed the ones that obviously didn't work -- too big, too white, too green/orange/purple. This left me with a lot of smaller buttons that might not have noticed before. It also allowed me to conclusively eliminate any that did not have at least three of a kind.
What I came up with are these, some of which you have seen before.
Red pearlies with shank:
Buttons with a shank might work better given the thickness of the garter stitch fabric. Styles with >3 items allow me to sew an extra button on an inside seam in case one gets lost.
Let the voting begin!