I've run into similar issues with drag and drop. Have you looked into
using ajax to redraw the chart anytime it's moved? This way you don't
have to reload the whole page and it only reloads the ones it needs.
We use the same layout you described to display charts and allow users
to move them around their dashboard. We already used ajax to display
the charts so it was simple extension to redraw anytime they were
moved. Depending on the data passed into the include file you might
be able to implement an ajax call that gets the contents of your
include file. I imagine the D&D plug-in you're using has an event hook
you can use to call the ajax function (we've been using the plugin
from JQuery UI).
Hope this helps! Good luck!
Mike