Tileable Normal Map Causing Hard Shadows on Beveled Edge with Static Lighting

Unfortunately, my above ‘solution’ was less of a good option than I thought. Everything looks fine when the light map resolution of my mesh is no higher than 64. Anything higher causes the hard line to reappear. Based upon some research, I tried reimporting the mesh with normals set to flat (right click in Blender, ‘Shade Flat’) and got the following result:

While the hard edges across the entire surface are perfectly expected, the odd lighting variations a little over half way up the side (roughly where the single hard edge was appearing before) are completely unexplainable to me. Does anyone else have some ideas?