Just to add a little clarification on the lens focal length of a GoPro versus a Mirrorless camera...
As you mentioned, the GoPro 35mm equivalent (the standard to compare focal lengths against) is about 16mm, however the 35mm equivalent of a 16mm lens for the cameras you have listed is 24mm (with an APS-C sensor crop factor of 1.5). To be closer in range of the GoPro FOV you would actually need about a 10mm lens... That being said, I like the FOV of the 16mm on the Sony mirrorless cameras.