OK, so after some further digging it looks like I'm probably not approaching this the right way. If I am getting this right now, the TRACE in C++ is simply a Visual Studio macro used for debugging. It looks like it does not allow one to direct the output elsewhere (and the output doesn't even print out anywhere for Release builds).
If I am getting all of that correct, it looks like my best bet here is probably to identify the most important trace points in the C++ side and provide a mechanism for passing the info to the C# code for trace logging.
Unless someone corrects me, I will mark this as the answer.