The only thing I really did different was cleanly merge the vertices & remove the now completely hidden faces.
I primarily work with models in a game engine, and intersecting geometry can cause some unpleasant artifacts when dealing with UVs. This is especially true of when dealing with material expressions at runtime, material blueprints in UE4 for example. Something to keep in mind 
As you can see, it just comes together at the vertices/edge-loop highlighted below and it is now a completely hollow model.
