So because I just love to throw money at problems
, I ordered both the silicone frame that Usafle
suggested in Post #6,and the bracket that Ops
suggested in Post #9.
First I tried the silicone frame.
It fit around the plate, and everything attached to the top sockets. The silicone did muffle things a bit when I'd close the liftgate, but everything did still vibrate.
So then I tried the bracket. As I feared, after playing around with it for an hour or two, I just couldn't get it to work either.
I was able to get screws fastened into the lower Euro sockets through the yellow slots, and the license plate itself fastened to the upper sockets through the red holes. But I couldn't figure out how to fasten the bottom holes in the plate through the blue holes -- I couldn't get a screw threaded into the blue holes without risking scratching the liftgate on the other side; and I couldn't fit a nut onto a bolt there without risking the same thing. And without anchoring the plate to those bottom yellow holes, there's no advantage to the bracket. Good idea, though!
So what I finally did was take the silicone frame, and sandwich it under the plate with my existing thin black steel frame on top. The plate is attached to the top sockets with black steel screws; and I'm still using the nylon nuts and bolts just to visually hide the bottom holes in the plate.
Between the stiffness of the metal frame and the vibration absorption of the silicone frame, everything is solid and quiet when I close the liftgate -- no vibration. Nice and solid.
Here's what the whole stack looks like -- you can see the grey silicone frame behind the plate, with the steel frame in front of it:
I'm sure the other methods (velcro, silicone pads) would work too, but this works for me...