I too am having issues with the landing page. Some times it will show and other times it will not. When I go to the theme’s “customize”, the landing page will most of the time not show in the preview pane even when enabled. When it doesn’t show in the preview pain it will not show on the front end. With the landing page enabled it acts like its disabled and the default WordPress home page is shows.
I have tried it in the latest versions of Chrome, Firefox and Explorer all with the same response.