I tried my new Edge 1050 in the special K -Edge mount for my ENVE bars, and I can just squeeze it by the stem. Fortunately the buttons are canted outward at the corners of the unit, so you can press them. Much better position than on the 1040. I was concerned about the fit in that mount because there’s no good alternative for those bars, with flattened tops.
Now I have to try it on my 3 other bikes, but they all have round bars.