Here are two campgrounds that we have used. They are about 20 minutes west of Disney just off of I4 and US 27. Its been a few years since I've been there, so I can't give a recent update as to there condition.
ThemeWorld RV resort
KOA Orlando SW Fort Summit
Keep trying By Telephone, Disney Fort Wilderness. I have had good luck on the phone, when the website says nothing is available. Get some days when you can and they keep phoning back, get more persistant in the fall when people that have previously booked, realized their plans have changed.
Book something now and then cancel or modify them when your Fort Wilderness plans have come together.
You definitely can't beat the Fort Wilderness experience, especially in the holiday seasons.
Ken
2006 Winnebago Outlook 29B E-450.
2012 Honda CR-V AWD
Blue Ox Aventa LX tow bar and Brake Buddy Vantage.