Thanks for verifying, that Britax III = MTC5084. Have the same problem (this metal thing broke after the mirror got in touch with an other mirror of a car comming the opposite direction). Currently I solved it by drilling through the arm (there is a hole in the ball anyway) and cut in a winding. Then I used a huge metal washer and a washer of the same size made of rubber on a screw to fit the housing on the arm. The idea was that the rubber gives tight connection between the housing and the metal washer, while the metal washer slips on the screw to prevent overtightening. Despite serious worries, this has been working perfectly for months. Just keep in mind always adjust the mirror clockwise (counterclockwise would loosen the screw). Of course there is no tilt function given by that method, but I found out that there is no need of that anyway.
