OK. Those are very narrow strips. What I would suggest is machine quilting down the center of the strips. Instead of square sewing, though (would make *lots* of stops and starts), make it continuous. I can't draw it here so don't know how to explain it. If I can find a pattern online, I will post it.
Log cabins can also look nice with circular quilting patterns (the curves of the quilting creating a nice contrast to the geometrics of the piecing) such as fans or all-over squiggles.