So I'm not having this exact problem (with the black screen) but I AM running into the problem were you cant add or remove plugins from Construct projects in XDK (which could be causing the black screen).
I've tried with the current and previous version of XDK.
I'm using the latest beta of Construct 2 also btw and the issue remains.
It is incredibly simply to reproduce for me - make a new Construct 2 project. I used the portrait HD. Exported via Cordova. Opened as new project in XDK - tried to add a plugin (core or 3rd party) and nothing happens. Also you cant remove plugins either.
Maybe I should open a new thread for clarity?