Hi Jonathan! First, EXCELLENT catch on this, sir. This will come as no surprise to those who know me, but you have officially ruined my Sunday! (LOL, just kidding).
Just when I thought I had it nailed, you come up with a pic showing that this particular greeb is definitely thicker than I thought. It's the first photo of a side view I've seen, and the shadow underneath it proves this IMO.
However, I don't think it was the same one used on Leia's DDC for a few reasons..
Although the thickness looks closer, the close-up in the first pic shows what seems to me a flat, square top, whereas the button has a smaller top with the sides angles inward. I could be wrong of course, as the blue arrow in the last pic shows what could be those sides, just unpainted.
But, there is still the rest of it to explain. The yellow arrows (3rd image) show some sort of clips(?) and although the top is level with the folding stock it is a different color (green arrows), leading me to believe it was one whole piece.
Unless we get one of the original prop makers involved (highly unlikely) I don't think we will ever know exactly what strange part was used, so I am thinking I may need to re-design my original.