I also have been having the same problem with a black screen appearing after the construct splash screen though mine is only if I add the Cordova WKWebView plugins in Intel XDK when trying to enable WKWebView on ios. I have tried a whole bunch of stuff with the new Intel XDK project format enabled and disabled. I have been trying to work it out over on the Intel forums but when I came across this I decided to download the capx and like Ashley I have no problems when I export the project in the XDK project format. It works on my iPhone both with and without WKWebView.
This leads to believe that if the Intel XDK project format adds all the necessary WKWebView plugins and settings and it definitely works (as proven above) then is there somehow a setting in Construct that can mess with Intel in regards to WKWebView? Perhaps its something if you made a project in the past and have updated Construct over time? (For instance I have been working on my project for 6 months and updated Construct as the updates have come out)