Don't try this at home kids. It will drive you nuts!
Thank you all for the input!! I'm sure that some of the suggestions here would have worked, but alas, the order in which I tried them was a critical factor. I first tried to hook the loop at the bottom and use the wall contour to close the arms. Unfortunately, this method bent the tips of the tongs inward. Definitely not the winning suggestion, or implementation of it, at least
The 2-noose idea would likely have worked if I had tried it first, but since the tips were bent, it just pulled off one of the silicone ends.
At this point of extreme frustration, it would normally be off to the recycler. It is just a cheap polycarbonate bottle. But since the post got so much interest, I am going to keep it around as a challenge for visitors and give updates. I'm also going to try a large wire noose around the bottom when I have some more time. Maybe that can bend the tips back to the right angle.
It's last beer was an American IPA dry hopped with Citra, obviously now called "Salad Tongs IPA". It is cold conditioning now and will probably taste like salad, garnished with tears of frustration.