A thought popped in my head 30 minutes ago while walking back toward the house with the dogs. The right half of the image attached here shows what was done on the Convertible and what should work without much if any change at all on a Road King (or other) windshield. On the left is the 14//15 Deluxe. The larger bracket that is part of the windshield mount on the front of the windshield isn't shown there but even with what's seen one can see that it's not as simple a through-windshield mount as is the Convertible. The emblem on the front of the Convertible windshield (green circle) is both part of the mount system to sandwich the windshield and it serves to decoratively cover all the work from the front.
However.... I was still thinking about some Road Glide mounting that would be better than the instrument nacelle mount and get it off the bars. First idea had been doing the same thing and going through the windshield. Unsure if distance from the rider might be a problem there or, since those screens don't have to be all that long, how much actual working real estate will be available. Then, while walking the dogs, had an idea. With either the part #14 from the Convertible exploded view or #23 from the Deluxe's image what about taking it from windshield facing and instead mounting it face down on and through the top of the inner fairing. Just above the radio and toward the rider. It would have the unit much closer to the radio. It would suspend above the radio as well.
Not sure if the screws in the axial joint on either mount tighten to the point of fixing motion or not. If they do there could be even less issue. If not might be a case of either finding a "happy" place where the bottom of the GPS hit the inner fairing such that the angle toward the rider was right. Might also drill and tap a hole through that bracket that accepts the AMP mount and run a long thumb screw it and use that for adjustment.
Will definitely need all the parts from the Convertible installation for the Road King. Think I'll go ahead and get #s 21, 22, and 23 from the Deluxe's installation as well then can mock up either set on the Road Glide to see if either will work or which one works better.