She does a one-day-a-week pullout gifted program which is really excellent, and the rest of her actual education is through her love of reading whatever fiction and non-fiction interests her (lots of library books, and lots of quality fiction and interesting history/science reference books at home), Ask magazine, BrainPop Jr, Monopoly, Snap Circuits, chess, Scrabble, geocaching, watching cool documentaries, YouTube (Vi Hart, space station), doing crosswords, traveling, hiking, star-gazing, visiting the planetarium and all those places Knitting Mama listed, badge-work for Brownies, long conversations with DH and I full of hard questions, sometimes I wantonly pull her out of school to join a science workshop run by the local homeschooling group … etc etc.
But I too hesitate to call it after-schooling because it's ALL DD-driven as and when she feels like it. I wouldn't set up anything formal - and admittedly she's ahead in all areas so there's no need - because her learning is part of her playing and I want to keep it that way.
Thank you for all the great educational activities and ideas in your original post.