Availability at SSR and probably OKW will not be a problem as they have more accessible units. (All the accessible rooms at SSR have roll-in showers, raised toilets and grab bars.)
Boardwalk, Beach Club and Wilderness Lodge have fewer rooms and consequently less availability. (I think Beach Club only has about 8 accessible rooms.) During the F&W festival the Boardwalk/Beach Club area is in high demand.
Getting accessible studios seem to be more of a problem than 1 bedrooms because of the cheaper point difference.
I need a fully accessible room for my travels (I need a roll-in shower), so my first request home (made last May for December) was an interesting experience. I had wanted to do an accessible studio at VWL. No rooms available, though they did have a non-accessible 1 bedroom. No studios at SSR either, but some accessible 1 bedrooms at BCV for part of my stay. I ended up getting an accessible 1 bedroom at SSR at 6.5 months out for the entire length of my stay. I even changed the ressies later to extend my trip without a hitch.
When you call to make your reservations, let the MS guide know you need an accessible room when you tell them the dates. They'll put you on hold, call special services and check on availability. It saves time if your pretty clear about what you need, where you want to go and when. Then you can authorize the MS agent to check availability and book the room. I've made 3 reservations so far (going again in May and October) with a mix of points, pay, weekends and weekdays and various accommodations. I call, tell them what I want, wait on hold for about 5 minutes and they get back to me with a confirmation number. I've even called back to add a day and had no problems.