I think you'll be ok with the possible exception of the dedicated 2 bedroom with 2Q's in the second bedroom. I don't know this as a fact, however! Best wishes!!!
Bobbi
PS. I am assuming you don't want 4th of July as I think that would be harder, period.
The week before the 4th can be a problem, too, but otherwise, I agree with Bobbi. Early June is usually easier than the other weeks of June and July. Late August is also a bit easier
We booked 7 months out and got a 1 bedroom for the middle of August no problem . We didn't even call day by day and I believe it wasn't exactly 7 months out, maybe a week after the 7 month date .
I was very surprised when I called last May for a 2 Bedroom in July. I not only got the two bedroom I got a dedicated queen room.... Now I wanted it over a weekend which may have helped!