Looked at an expensive (> $55) mobile phone cradle to use with the big Lumia 1520. It's a suction cup mount with an adhesive suction surface that can apparently/allegedly cling to rough/uneven surfaces. Next there's a swivelling ball joint & a very powerful magnetic plate of about one square inch in area. The kit comes with two very thin steel sheets that are stuck to the back of the phone (one on the phone & one spare), and can fit between the phone & any case it might be in.
But that was too expensive/complex. The lumia 1520 is 3½ inches wide, the adaptor I chose can open to at least 4 inches. This one was chosen for that reason & that it would fit my current windscreen mount.