It looks like having the JustMock profiler enabled when attempting to work on .NET Core projects causes some kind of issue that makes it impossible to compile or run the code.
I had the exact same issue detailed here: http://www.lpaneque.com/2016/05/justmock-and-failed-to-initialize-coreclr.html and disabled the profiler (just like the author) and I was able to successfully develop .NET core apps after.