I've found that, in order to rid those white outline edges, you need to color the opposite untextured face with...the correlating texture. OR erase extra triangles that were formed when altering a structure. It's a rather...minute fix, and may add more time, but is a subtle way to make your maps cleaner. IF you want to do that.
unless you do know that, then my comment is irrelevant.
if you do this, be wary what program you are using. it may make programs like HT a little challenging bc it will not allow you to see behind textured surfaces.
--interesting project overall, as well as concepts