Take a look at the local public school. You may find that the Middle school is much much better - a whole different animal than the elementary. It maybe worth it in terms of 'free babysitting' with Afterschooling.
I would certainly talk to the Independent school and ask if they have block on sites to games, etc. How many Middle school students left last year due to the changes? Does the Independent school have a High School attached to it? Look ahead to the good High School programs and ask them which Middle schools do a good job of preparing their students.
Best Wishes,
Grinity