Cut pieces of vibration dampening material, be it foam tape or butyl mat.
Place (4) 1.5"x.75" pieces where the 4 fins rub against the shelf.
Take a roll of .25 foam weatherstrip and adhere it to the trailing edge of the plastic shelf covering (topside where it meets the window).
Cut another 1.5"x3" piece of butyl mat or foam tape and adhere it where the keyless module
Install everything in reverse order of removing it.
Drive around and ask yourself, "Why the hell didn't I do this before".