We have been twice in July,once before & during the 4th and once after.GO AFTER!!!!!!
Our best trip was July 6-10(going home the 11th),and the worst(crowd wise)was June 29-July4(going home the 5th).I think everybody came for the 4th and they all left right after(like we did the second trip)so when we went on the 6th,it was awesome!MUCH less crowded than going the week before the 4th,and the 4th itself was mobbed!
We still had a great time when we went June 29-July 4,and I'm sure you will too whenever you go,it was just less crowded and crazy right AFTER the 4th.