Ground Wires Connected Outside of Switch Box
I trrust and hope that the ground wires are indeed connected together out there, with a crimp ring or wire nut or clamp as opposed to merely being twisted together.
I would try to find some kind of small screw-tightened clamp that will fit on one of the other (bare) ground wires without nicking it and tie the ground wire of (or a bare pigtail to) the new device's ground.
The disadvantages of crab apple trees. In summer, the apples are too sour to pick and eat. In winter the birds come and leave dropping all over the place.