Avenged:
Yea so I was pretty cooked on the bestagon metric when it finally hit me.  Overlap solves basically every challenge in this puzzle.  After realizing this I setout to make my first overlap solution, effectively allowing me to lower the bestagon one unit lower than possible otherwise and solving many of the annoyances making my current scoring solution difficult to improve.  Area can be improved but this is the classic bestagon / aesthetics / overlap category