Actually most times you can park closer than you think by getting to the parks later in the day. We are not morning people and never get to any park before 11 am. We always have a car. Sometimes we park really close because people who have been there at opening are already leaving! August is not a very busy time, we have gone for the past ten years and have NEVER had a problem with parking. Even during Easter, the past two years anyway, we were amazed at how easy parking was. All this being said, sometimes the CMS won't let you drive all the way to the front even though there are tons of empty parking spaces. But, not to worry! As the above post said, trams are available and you never have to walk or wait very long. We love having our own car, so much easier and comfortable than buses. I don't think you will have any problems.
Have a wonderful vacation!!!