There are no more slow times at WDW. Attendance is past where it was pre 9-11. The parks won't be 4th of July busy but don't expect to walk on RnRC at 5:00 PM. Get to the parks early, use fast pass and make your ADR's ahead of time.
I go the first week in March each year and the lines are not too bad. The ESPN weekend is one week before you are going, so I don't know if that will effect the crowds or not.