The jogging stroller "ban" was being discussed on the boards in about August of 2002. It was the jogging strollers with the single big front wheel that were the problem. For a short time, people with those jogging strollers were being asked to "tradde" their stroller for the day for a WDW stroller (free of charge). Some people who emailed WDW were told the same information.
But, the ban doesn't seem to have continued.
We were at WDW last March and also my DH and I were there in July 2003. We did see those jogging strollers in use in the parks. I have also seen posts from people who saw them when they went and from people who said they took their jogging strollers (although I am not sure that all those people had the big wheel version).
Because you have a special needs child who can't sit in a regular stroller, your stroller would be an exception to the rules (even if they are banning those type of strollers). Your stroller is a mobility device that they can't restrict according to the ADA (American with Disabilities Act).
But, because I do know that the Baby Jogger company makes a small set of swivel wheels that is easily exchangeable with the large front wheel. The large wheel is really meant for joggin or off-sidewalk use and the smaller swivel wheels are more suitable for WDW. I would suggest getting a set of the small swivel wheels if possible because you will find it much easier to manouver around WDW with them.
If you do bring the stroller, stop at Guest Services in any of the parks to ask for a Guest Assistance Card that will allow the stroller to be used as a wheelchair. That way, you will be allowed to bring it into queues where strollers would not normally be allowed.
We've never used one (when DD was little, they didn't have any canopies for wheelchairs), but there are companies that make wheelchair canopies if you want to investigate that option if your DD would be more comfortable in her wheelchair.
Here's a link to one company.
And another.
And an umbrella (a less expensive option).
And an umbrella holder that you use with your own umbrella.
I've also seen people with umbrella holders meant for strollers attached to their wheelchair to hold an umbrella.