If you're set on using EP4IR, I think the question boils down to: how can you call non-.NET C++ code in C#. From a prior stack overflow thread, it looks like there are a few ways to do this, including using P/Invoke or writing a C++.NET wrapper around the non-.NET code you want to call. C++.NET was specifically designed to make it easy to call legacy non-.NET code.
If you are willing to try out other dependency representations, you might want to take a look at Antelope. It's a rather complete .NET based natural language processing toolkit. It'll allow you to use both the Link parser (demo) and the Stanford Parser (demo). Both of these will give you a reasonably good typed dependency representation for a sentence.