We spent last 4th of July at Vero, and it was great! It's very hot, but definitely more comfortable than WDW at that time of year. Plus, they've closed off Stormalong Bay to pool hopping that week, so if you went to OKW you wouldn't be able to hop to the best pool at wdw. Since AK is the only park you've got access to with your passes, and AK is so darn miserable in the summer (HOT, HOT, HOT), I say stay far away from wdw the entire 4th of July week....you're much better off at Vero.
Enjoy! We'll be there a week after you - staying in an Inn room. I like the Inn rooms much better than the studios - maybe you'll get to stay without moving if you ask at check-in.