For me the edge-split modifier did not work at all (not applied!). Perhaps related to the 2.79 version? Took me a lot of time to find out that the SubSurfModifier did the job with the Simple option checked. Gets rid of the triangles. My settings are:
Here you can see from left to right the topology, the final render with subsurf subdivisions at 2 and the preview render with the subdivisions at 1. In the latter you see the triangles. When you set them both to subdivions 2 there are no triangles in the preview render either.
