I tinkered with the grip mechanism and it works much better. The piano hinge returns and is inverted; the chain is gone and is replaced with a slider. I was thinking of adding magnets to keep the grip from moving around, but the elastic band provides enough friction that it probably won't be necessary.

To deploy the grip, simply squeeze the bottom (well, the top as I have it upside down in the photo) together and it will slide into place. To put it back, just pull it down and push the sides back into position.