I think changing config.xml and src/config.json in the app, and then the setting in Moodle, should be enough to make it work (at least with Phonegap Build).
If you're generating the app in a local environment, you need to modify the config.xml file BEFORE running cordova prepare, since the URL_SCHEME is set when installing the plugin cordova-plugin-customurlscheme. You can also remove the plugin and add it again passing the scheme as a variable in the command:
cordova plugin add cordova-plugin-customurlscheme --variable URL_SCHEME=myscheme
The app should detect if the SSO needs to be performed using local_mobile or not. If core supports SSO login then the app should use it instead of local_mobile, regardless of the value in wsextservice.
When connecting to a site the app will always try to use https first. If it fails, then it will fallback to http. Once the app determines if the site uses http or https then it should always stick to that unless your site specifies a different httpswwwroot.