Well, Sunday in MK is now an early entry day, so those results you found may be a bit scewed.
We went to MK on Sunday in October, after the EE was reinstated. We didn't get there until 11 am, and mostly stayed in the front area where all of the characters were signing autographs. The only lands to which we went were Adventureland and Liberty Square, which weren't crowded at all. DH and I rode Pirates of the Caribbean with practically no wait at all, my parents, DD and I rode Aladdin with about a 10 minute wait, and my parents took DD (8) to see the Hall of Presidents (she was NOT impressed), with no wait. I don't know how well the rest of the park was faring. However, if you go for EE morning, you can knock out Fantasyland, and part of Tomorrowland (get a FP for Space Mountain and come back) in the 1st hour, then get quickly over for the rope drop for Frontierland and line up for either Splash Mountain or Big Thunder. After those go back and use your FP for Space Mountain, swing into Adventureland and ride (the lines won't be overly long), then go to the Haunted Mansion. After all of that, it should be about time to line up to see the parade... or if you aren't interested in the parade, it is always a good time to ride, as the line decrease considerably.
I don't think you will have a problem going to MK on Sunday. Have a good vacation!