I don't think I've ever been at CP on or near a holiday and not faced a capacity crowd. Add that to the MF factor this season, and you have a recipe for disaster.
The 4th is a Tuesday this year, though, so maybe the crowds won't be as bad, since people will likely have to work the next day. Still, if you're driving any non-trivial distance to CP, I wouldn't chance it.
Personally, I'm aiming my trip for June 25-29 (including two days of driving from Kansas City, round trip). I'd be at the park Monday through Wednesday. Anyone have opinions on that?